Exam 21: Complex Numbers

Combine the vectors: $40 \angle 75^{\circ}+64 \angle 130^{\circ}$

Combine and simplify: $\left(\frac{2}{3}+j \frac{3}{2}\right)-\left(\frac{3}{2}+j \frac{2}{3}\right)$

Evaluate: $\sqrt[5]{32 \angle 120^{\circ}}$

Write ${ }^{8-j 6}$ in polar and trigonometric form.

Combine the vectors $16 / \underline{11^{\circ}}+23 / \underline{70^{\circ}}$ . Write the answer in rectangular form.

Write $9+j 5$ in polar and trigonometric form.

Multiply: $\left(8.5 \angle 235^{\circ}\right)\left(12.4 \angle 190^{\circ}\right)$

Evaluate: $\left(3 e^{\mathrm{j} 3}\right)^{3}$

Express in sinusoidal form: $V=75 \angle 32^{\circ}$

Evaluate: $\sqrt{25+j 32}$

Multiply: $8\left(\cos 36^{\circ}+j \sin 36^{\circ}\right)$ by $2\left(\cos 63^{\circ}+j \sin 63^{\circ}\right)$

Express $7.5 e^{j 2.7}$ in rectangular form. Use three significant digits.

Graph this complex number: $-4+\mathrm{j} 6$

Graph the complex number $1+j$ .

Write $8-\mathrm{j} 6$ in polar form. Use three significant digits.

Evaluate: $j^{26}$

Evaluate: $j^{2008}$

Evaluate: $\left(5 / \underline{40^{\circ}}\right)^{3}$

Multiply and simplify: $\sqrt{-9}(4-\sqrt{-36})$

Multiply and simplify: $(3+2 j)^{3}$