Question 1

Multiply: $4.5 e^{j \frac{\pi}{3}} \times 7.1 e^{j \frac{3 \pi}{4}}$

Accepted Answer

$31.95 e^{j \frac{13 \pi}{12}}$

Question 2

Write $6\left(\cos 82^{\circ}+j \sin 82^{\circ}\right)$ in rectangular and polar form.

Accepted Answer

$0.835+\mathrm{j} 5.94,6 / \underline{82^{\circ}}$

Question 3

Multiply and simplify: $\sqrt{-98} \times \sqrt{-32}$

Accepted Answer

$j 56$

Question 4

Evaluate: $\left[3\left(\cos 55^{\circ}+j \sin 55^{\circ}\right)\right]^{4}$

Accepted Answer

The answer of Evaluate: $\left[3\left(\cos 55^{\circ}+j \sin 55^{\circ}\right)\right]^{4}$...

Question 5

Solve for $x$ to three significant digits: $x^{2}+x+40=0$

Accepted Answer

The answer of Solve for $x$ to three significant digits:...

Question 6

Find the complex impedance $Z$ in the figure below:

Accepted Answer

The answer of Find the complex impedance $Z$ in the...

Question 7

Evaluate: $\left(4 / \underline{112^{\circ}}\right)^{2}$

Accepted Answer

The answer of Evaluate: $\left(4 / \underline{112^{\circ}}\right)^{2}$...

Question 8

Solve for $\mathrm{y}$ to three significant digits: $3.2 y^{2}-6.1 y+12.7=0$

Accepted Answer

The answer of Solve for $\mathrm{y}$ to three significant digits:...

Question 9

Write as a complex number in rectangular form: $\sqrt{-\frac{16}{25}}+8$

Accepted Answer

The answer of Write as a complex number in rectangular...

Question 10

Combine and simplify: $(16+j 27)-(8-j 16)$

Accepted Answer

The answer of Combine and simplify: $(16+j 27)-(8-j 16)$...

Question 11

Express the voltage $v = 4/\underline{30^\circ}$ in sinusoidal form

Accepted Answer

The answer of Express the voltage $v = 4/\underline{30^\circ}$ in...

Question 12

Multiply and simplify: $(2+j 8)(3-j 6)$

Accepted Answer

The answer of Multiply and simplify: $(2+j 8)(3-j 6)$...

Question 13

Factor $x^{2}+81$ into complex factors.

Accepted Answer

The answer of Factor $x^{2}+81$ into complex factors....

Question 14

Express in complex form: $i=48 \sin \left(\omega t+121^{\circ}\right)$. Use three significant digits.

Accepted Answer

The answer of Express in complex form: \(i=48 \sin \left(\omega...

Question 15

Write ${-15-j 22}$ in polar and trigonometric form.

Accepted Answer

The answer of Write ${-15-j 22}$ in polar and trigonometric...

Question 16

Combine the vectors: $85 \angle 275^{\circ}-50 \angle 144^{\circ}$

Accepted Answer

The answer of Combine the vectors: \(85 \angle 275^{\circ}-50 \angle...

Question 17

Write in rectangular and trigonometric form: $8 /-50^{\circ}$. Use three significant digits for rectangular.

Accepted Answer

The answer of Write in rectangular and trigonometric form: \(8...

Question 18

Express $8\left(\cos 60^{\circ}+j \sin 60^{\circ}\right)$ in exponential form.

Accepted Answer

The answer of Express $8\left(\cos 60^{\circ}+j \sin 60^{\circ}\right)$ in exponential...

Question 19

Combine the vectors: $4\left(\cos 15^{\circ}+j \sin 15^{\circ}\right)+3\left(\cos 35^{\circ}+j \sin 35^{\circ}\right)$

Accepted Answer

The answer of Combine the vectors: \(4\left(\cos 15^{\circ}+j \sin 15^{\circ}\right)+3\left(\cos...

Question 20

Divide and simplify: (3 - j11) ÷ (5 + j6)

Accepted Answer

The answer of Divide and simplify: (3 - j11) ÷...

Exam 21: Complex Numbers

Multiply: 4.5ejπ3×7.1ej3π44.5 e^{j \frac{\pi}{3}} \times 7.1 e^{j \frac{3 \pi}{4}}4.5ej3π​×7.1ej43π​

Write 6(cos⁡82∘+jsin⁡82∘)6\left(\cos 82^{\circ}+j \sin 82^{\circ}\right)6(cos82∘+jsin82∘) in rectangular and polar form.

Multiply and simplify: −98×−32\sqrt{-98} \times \sqrt{-32}−98​×−32​

Evaluate: [3(cos⁡55∘+jsin⁡55∘)]4\left[3\left(\cos 55^{\circ}+j \sin 55^{\circ}\right)\right]^{4}[3(cos55∘+jsin55∘)]4

Solve for xxx to three significant digits: x2+x+40=0x^{2}+x+40=0x2+x+40=0

Find the complex impedance ZZZ in the figure below:

Evaluate: (4/112∘‾)2\left(4 / \underline{112^{\circ}}\right)^{2}(4/112∘​)2

Solve for y\mathrm{y}y to three significant digits: 3.2y2−6.1y+12.7=03.2 y^{2}-6.1 y+12.7=03.2y2−6.1y+12.7=0

Write as a complex number in rectangular form: −1625+8\sqrt{-\frac{16}{25}}+8−2516​​+8

Combine and simplify: (16+j27)−(8−j16)(16+j 27)-(8-j 16)(16+j27)−(8−j16)

Express the voltage v=4/30∘‾v = 4/\underline{30^\circ}v=4/30∘​ in sinusoidal form

Multiply and simplify: (2+j8)(3−j6)(2+j 8)(3-j 6)(2+j8)(3−j6)

Factor x2+81x^{2}+81x2+81 into complex factors.

Express in complex form: i=48sin⁡(ωt+121∘)i=48 \sin \left(\omega t+121^{\circ}\right)i=48sin(ωt+121∘) . Use three significant digits.

Write −15−j22{-15-j 22}−15−j22 in polar and trigonometric form.

Combine the vectors: 85∠275∘−50∠144∘85 \angle 275^{\circ}-50 \angle 144^{\circ}85∠275∘−50∠144∘

Write in rectangular and trigonometric form: 8/−50∘8 /-50^{\circ}8/−50∘ . Use three significant digits for rectangular.

Express 8(cos⁡60∘+jsin⁡60∘)8\left(\cos 60^{\circ}+j \sin 60^{\circ}\right)8(cos60∘+jsin60∘) in exponential form.

Combine the vectors: 4(cos⁡15∘+jsin⁡15∘)+3(cos⁡35∘+jsin⁡35∘)4\left(\cos 15^{\circ}+j \sin 15^{\circ}\right)+3\left(\cos 35^{\circ}+j \sin 35^{\circ}\right)4(cos15∘+jsin15∘)+3(cos35∘+jsin35∘)

Divide and simplify: (3 - j11) ÷ (5 + j6)

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