Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 10 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \\ w = 5 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right) \end{array}\] Find zw.

A) $5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ B) $50 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ C) $50 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ D) $5 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right)$ A) $5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ B) $50 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ C) $50 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ D) $5 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right)$

Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 1 - i \\ w = 1 - \sqrt { 3 } i \end{array}\] Find $\frac { z } { w }$.

A) $\frac { \sqrt { 2 } } { 2 } \left( \cos 75 ^ { \circ } + i \sin 75 ^ { \circ } \right)$ B) $\frac { 1 } { 2 } \left( \cos 75 ^ { \circ } + \mathrm { i } \sin 75 ^ { \circ } \right)$ C) $\frac { \sqrt { 2 } } { 2 } \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)$ D) $\frac { 1 } { 2 } \left( \cos 15 ^ { \circ } + \mathrm { i } \sin 15 ^ { \circ } \right)$ A) $\frac { \sqrt { 2 } } { 2 } \left( \cos 75 ^ { \circ } + i \sin 75 ^ { \circ } \right)$ B) $\frac { 1 } { 2 } \left( \cos 75 ^ { \circ } + \mathrm { i } \sin 75 ^ { \circ } \right)$ C) $\frac { \sqrt { 2 } } { 2 } \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)$ D) $\frac { 1 } { 2 } \left( \cos 15 ^ { \circ } + \mathrm { i } \sin 15 ^ { \circ } \right)$

Exam 8: Polar Coordinates; Vectors

Graph the polar equation. - $r = \frac { 4 } { 1 - \sin \theta }$ $Graph the polar equation. - r = \frac { 4 } { 1 - \sin \theta } A) B) C) D)$ A) $Graph the polar equation. - r = \frac { 4 } { 1 - \sin \theta } A) B) C) D)$ B) $Graph the polar equation. - r = \frac { 4 } { 1 - \sin \theta } A) B) C) D)$ C) $Graph the polar equation. - r = \frac { 4 } { 1 - \sin \theta } A) B) C) D)$ D) $Graph the polar equation. - r = \frac { 4 } { 1 - \sin \theta } A) B) C) D)$

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Question 201

Write the expression in the standard form a + bi. - $( \sqrt { 3 } + i ) ^ { 5 }$

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Question 202

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $r=6 \cos \theta$ $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r=6 \cos \theta A) (x-3)^{2}+y^{2}=9 ; circle, radius 3 center at (3,0) in rectangular coordinates B) x^{2}+(y+3)^{2}=9 ; circle, radius 3 center at (0,-3) in rectangular coordinates C) (x+3)^{2}+y^{2}=9 ; circle, radius 3 , center at (-3,0) in rectangular coordinates D) \mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9 ; circle, radius 3 , center at (0,3) in rectangular coordinates$ A) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r=6 \cos \theta A) (x-3)^{2}+y^{2}=9 ; circle, radius 3 center at (3,0) in rectangular coordinates B) x^{2}+(y+3)^{2}=9 ; circle, radius 3 center at (0,-3) in rectangular coordinates C) (x+3)^{2}+y^{2}=9 ; circle, radius 3 , center at (-3,0) in rectangular coordinates D) \mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9 ; circle, radius 3 , center at (0,3) in rectangular coordinates$ $(x-3)^{2}+y^{2}=9 ;$ circle, radius 3 center at $(3,0)$ in rectangular coordinates B) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r=6 \cos \theta A) (x-3)^{2}+y^{2}=9 ; circle, radius 3 center at (3,0) in rectangular coordinates B) x^{2}+(y+3)^{2}=9 ; circle, radius 3 center at (0,-3) in rectangular coordinates C) (x+3)^{2}+y^{2}=9 ; circle, radius 3 , center at (-3,0) in rectangular coordinates D) \mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9 ; circle, radius 3 , center at (0,3) in rectangular coordinates$ $x^{2}+(y+3)^{2}=9 ;$ circle, radius 3 center at $(0,-3)$ in rectangular coordinates C) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r=6 \cos \theta A) (x-3)^{2}+y^{2}=9 ; circle, radius 3 center at (3,0) in rectangular coordinates B) x^{2}+(y+3)^{2}=9 ; circle, radius 3 center at (0,-3) in rectangular coordinates C) (x+3)^{2}+y^{2}=9 ; circle, radius 3 , center at (-3,0) in rectangular coordinates D) \mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9 ; circle, radius 3 , center at (0,3) in rectangular coordinates$ $(x+3)^{2}+y^{2}=9$ ; circle, radius 3 , center at $(-3,0)$ in rectangular coordinates D) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r=6 \cos \theta A) (x-3)^{2}+y^{2}=9 ; circle, radius 3 center at (3,0) in rectangular coordinates B) x^{2}+(y+3)^{2}=9 ; circle, radius 3 center at (0,-3) in rectangular coordinates C) (x+3)^{2}+y^{2}=9 ; circle, radius 3 , center at (-3,0) in rectangular coordinates D) \mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9 ; circle, radius 3 , center at (0,3) in rectangular coordinates$ $\mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9$ ; circle, radius 3 , center at $(0,3)$ in rectangular coordinates

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Question 203

Write the expression in the standard form a + bi. - $( 1 - i ) ^ { 10 }$

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Question 204

Graph the polar equation. - $r = \frac { 4 } { 4 - 2 \cos \theta }$ $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \cos \theta } A) B) C) D)$ A) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \cos \theta } A) B) C) D)$ B) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \cos \theta } A) B) C) D)$ C) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \cos \theta } A) B) C) D)$ D) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \cos \theta } A) B) C) D)$

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Question 205

Use the figure below. Determine whether the given statement is true or false. -H + I + J = B

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Question 206

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 6 + 2 \sin \theta ;$ the line $\theta = \frac { \pi } { 2 }$

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Question 207

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( - 1,0,2 ) , \mathrm { P } _ { 2 } ( 2,1 , - 2 ) , \mathrm { P } _ { 3 } ( 2 , - 1,4 )$

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Question 208

Find the position vector for the vector having initial point P and terminal point Q. -P = (-3, 2, -3) and Q = (2, 0, 1)

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Question 209

Plot the point given in polar coordinates. - $\left(-4,405^{\circ}\right)$ $Plot the point given in polar coordinates. - \left(-4,405^{\circ}\right) A) B) C) D)$ A) $Plot the point given in polar coordinates. - \left(-4,405^{\circ}\right) A) B) C) D)$ B) $Plot the point given in polar coordinates. - \left(-4,405^{\circ}\right) A) B) C) D)$ C) $Plot the point given in polar coordinates. - \left(-4,405^{\circ}\right) A) B) C) D)$ D) $Plot the point given in polar coordinates. - \left(-4,405^{\circ}\right) A) B) C) D)$

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Question 210

Solve the problem. Leave your answer in polar form. - z=10 4+i4 w=5 1+i1 Find zw.

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Question 211

Solve the problem. Leave your answer in polar form. - z=1-i w=1-i Find $\frac { z } { w }$ .

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Question 212

Graph the polar equation. - $r=\csc \theta-2,0<\theta<\pi$ $Graph the polar equation. - r=\csc \theta-2,0<\theta<\pi A) B) C) D)$ A) $Graph the polar equation. - r=\csc \theta-2,0<\theta<\pi A) B) C) D)$ B) $Graph the polar equation. - r=\csc \theta-2,0<\theta<\pi A) B) C) D)$ C) $Graph the polar equation. - r=\csc \theta-2,0<\theta<\pi A) B) C) D)$ D) $Graph the polar equation. - r=\csc \theta-2,0<\theta<\pi A) B) C) D)$

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Question 213

Find the unit vector having the same direction as v. - $\mathbf { v } = 7 \mathbf { i }$

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Question 214

Write the complex number in rectangular form. - $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

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Question 215

State whether the vectors are parallel, orthogonal, or neither. -v = 2i - j, w = 4i - 2j

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Question 216

Solve the problem. Round your answer to the nearest tenth. -Find the work done by a force of 6 pounds acting in the direction of 43° to the horizontal in moving an object 6 feet from (0, 0) to (6, 0).

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Question 217

Find the angle between v and w. Round your answer to one decimal place, if necessary. -v = -4i, w = j

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Question 218

Plot the complex number in the complex plane. - $- 6 i$ A) B) C) D)

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Question 219

Plot the point given in polar coordinates. - $\left[-2, \frac{-3 \pi}{4}\right.$ $Plot the point given in polar coordinates. - \left[-2, \frac{-3 \pi}{4}\right. A) B) C) D)$ A) $Plot the point given in polar coordinates. - \left[-2, \frac{-3 \pi}{4}\right. A) B) C) D)$ B) $Plot the point given in polar coordinates. - \left[-2, \frac{-3 \pi}{4}\right. A) B) C) D)$ C) $Plot the point given in polar coordinates. - \left[-2, \frac{-3 \pi}{4}\right. A) B) C) D)$ D) $Plot the point given in polar coordinates. - \left[-2, \frac{-3 \pi}{4}\right. A) B) C) D)$

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Question 220

Showing 201 - 220 of 270

Write the expression in the standard form a + bi. - $( \sqrt { 3 } + i ) ^ { 5 }$

Write the expression in the standard form a + bi. - $( 1 - i ) ^ { 10 }$

Use the figure below. Determine whether the given statement is true or false. -H + I + J = B

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 6 + 2 \sin \theta ;$ the line $\theta = \frac { \pi } { 2 }$

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( - 1,0,2 ) , \mathrm { P } _ { 2 } ( 2,1 , - 2 ) , \mathrm { P } _ { 3 } ( 2 , - 1,4 )$

Find the position vector for the vector having initial point P and terminal point Q. -P = (-3, 2, -3) and Q = (2, 0, 1)

Solve the problem. Leave your answer in polar form. - z=10 4+i4 w=5 1+i1 Find zw.

Solve the problem. Leave your answer in polar form. - z=1-i w=1-i Find $\frac { z } { w }$ .

Find the unit vector having the same direction as v. - $\mathbf { v } = 7 \mathbf { i }$

Write the complex number in rectangular form. - $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

State whether the vectors are parallel, orthogonal, or neither. -v = 2i - j, w = 4i - 2j

Solve the problem. Round your answer to the nearest tenth. -Find the work done by a force of 6 pounds acting in the direction of 43° to the horizontal in moving an object 6 feet from (0, 0) to (6, 0).

Find the angle between v and w. Round your answer to one decimal place, if necessary. -v = -4i, w = j

Plot the complex number in the complex plane. - $- 6 i$ A) B) C) D)

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Exam 8: Polar Coordinates; Vectors

Graph the polar equation. - r=41−sin⁡θr = \frac { 4 } { 1 - \sin \theta }r=1−sinθ4​ A) B) C) D)

Write the expression in the standard form a + bi. - (3+i)5( \sqrt { 3 } + i ) ^ { 5 }(3​+i)5

Write the expression in the standard form a + bi. - (1−i)10( 1 - i ) ^ { 10 }(1−i)10

Graph the polar equation. - r=44−2cos⁡θr = \frac { 4 } { 4 - 2 \cos \theta }r=4−2cosθ4​ A) B) C) D)

Use the figure below. Determine whether the given statement is true or false. -H + I + J = B

Test the equation for symmetry with respect to the given axis, line, or pole. - r=6+2sin⁡θ;r = 6 + 2 \sin \theta ;r=6+2sinθ; the line θ=π2\theta = \frac { \pi } { 2 }θ=2π​

Find the area of the parallelogram. - P1(−1,0,2),P2(2,1,−2),P3(2,−1,4)\mathrm { P } _ { 1 } ( - 1,0,2 ) , \mathrm { P } _ { 2 } ( 2,1 , - 2 ) , \mathrm { P } _ { 3 } ( 2 , - 1,4 )P1​(−1,0,2),P2​(2,1,−2),P3​(2,−1,4)

Find the position vector for the vector having initial point P and terminal point Q. -P = (-3, 2, -3) and Q = (2, 0, 1)

Plot the point given in polar coordinates. - (−4,405∘)\left(-4,405^{\circ}\right)(−4,405∘) A) B) C) D)

Solve the problem. Leave your answer in polar form. - z=10 4+i4 w=5 1+i1 Find zw.

Solve the problem. Leave your answer in polar form. - z=1-i w=1-i Find zw\frac { z } { w }wz​ .

Graph the polar equation. - r=csc⁡θ−2,0<θ<πr=\csc \theta-2,0<\theta<\pir=cscθ−2,0<θ<π A) B) C) D)

Find the unit vector having the same direction as v. - v=7i\mathbf { v } = 7 \mathbf { i }v=7i

Write the complex number in rectangular form. - 6(cos⁡330∘+isin⁡330∘)6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)6(cos330∘+isin330∘)

State whether the vectors are parallel, orthogonal, or neither. -v = 2i - j, w = 4i - 2j

Solve the problem. Round your answer to the nearest tenth. -Find the work done by a force of 6 pounds acting in the direction of 43° to the horizontal in moving an object 6 feet from (0, 0) to (6, 0).

Find the angle between v and w. Round your answer to one decimal place, if necessary. -v = -4i, w = j

Plot the complex number in the complex plane. - −6i- 6 i−6i A) B) C) D)

Plot the point given in polar coordinates. - [−2,−3π4\left[-2, \frac{-3 \pi}{4}\right.[−2,4−3π​ A) B) C) D)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Write the expression in the standard form a + bi. - $( \sqrt { 3 } + i ) ^ { 5 }$

Write the expression in the standard form a + bi. - $( 1 - i ) ^ { 10 }$

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 6 + 2 \sin \theta ;$ the line $\theta = \frac { \pi } { 2 }$

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( - 1,0,2 ) , \mathrm { P } _ { 2 } ( 2,1 , - 2 ) , \mathrm { P } _ { 3 } ( 2 , - 1,4 )$

Solve the problem. Leave your answer in polar form. - z=1-i w=1-i Find $\frac { z } { w }$ .

Find the unit vector having the same direction as v. - $\mathbf { v } = 7 \mathbf { i }$

Write the complex number in rectangular form. - $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

Plot the complex number in the complex plane. - $- 6 i$ A) B) C) D)