Exam 21: Complex Numbers

Solve for $x$ to three significant digits: $x^{2}-2 x+5=0$

Write this complex number in polar and trigonometric form: $1+j 9$

Express in complex form: v = 231 sin wt

Express in sinusoidal form: $V = 50/\underline{85^\circ}$

Combine the vectors: $(2-j 7)-(-9-j 2)$

Multiply and simplify: $j 3 \cdot(4-j 2)$

Write the complex conjugate of this complex number: $a+j b$

Express in rectangular, polar, and trigonometric form: $4 e^{\mathrm{j} 2}$

Solve for $x$ to three significant digits: $5 x^{2}-3 x+1=0$

Divide and simplify: $\frac{4+j 5}{-2+j}$

Divide: $28\left(\cos 65^{\circ}+j \sin 65^{\circ}\right) \div 7\left(\cos 150^{\circ}+j \sin 150^{\circ}\right)$

Combine the vectors $5\left(\cos 35^{\circ}+j \sin 35^{\circ}\right)-4\left(\cos 5^{\circ}+j \sin 5^{\circ}\right)$ , write your answer in rectangular form.

Write a sinusoidal expression for the current $i$ in the figure below:

Solve for $x$ to three significant digits: $5 x^{2}=4 x-17$

Write $10+j 2$ in polar and trigonometric form.

Write in rectangular form: $32 /\underline{240^{\circ}}$

Divide: $\frac{12.5 e^{j \frac{3 \pi}{4}}}{2.5 e^{j \frac{\pi}{8}}}$

Multiply: $8 e^{\mathrm{j} 2.5}$ by $3 e^{\mathrm{j} 1.1}$

Multiply and simplify: $(4-9 j)^{2}$

Express the current $i=45 \sin \left(w t+32^{\circ}\right)$ in complex form.