Exam 21: Complex Numbers

Write as an imaginary number: $\sqrt{-25}$

Evaluate: $\sqrt[3]{4 / \underline{114^{\circ}}}$

Write as a complex number in rectangular form: $2+\sqrt{-9}$

Write ${-11+j 17}$ in polar and trigonometric form.

Express 10 - j16 in exponential form.

Divide: $12\left(\cos 22^{\circ}+j \sin 22^{\circ}\right)$ by $3\left(\cos 12^{\circ}+j \sin 12^{\circ}\right)$

Evaluate: $j^{79}$

Factor $2 x^{2}+18$ into complex factors.

Express the voltage $v=10 \underline{-90^{\circ}}$ in sinusoidal form.

Combine the vectors: $6.4 / \underline{38.7^{\circ}}+10.4 / \underline{343.3^{\circ}}$

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

Multiply and simplify: $(5-\sqrt{-4})(\sqrt{-64}-8)$

Express $12 e^{j \frac{5 \pi}{4}}$ in rectangular form.

Write in rectangular and trigonometric form: $4 / \underline{112^{\circ}}$

Write $\sqrt{-\frac{9}{16}}$ as a complex number.

Divide the vectors: $\left(9.2 / 74^{\circ}\right) \div\left(29 / 51^{\circ}\right)$

Evaluate: $\sqrt{9 / 60^{\circ}}$

Evaluate: $\left[3\left(\cos 25^{\circ}+j \sin 25^{\circ}\right)\right]^{3}$

Multiply the vectors: $\left(8 / 75^{\circ}\right) \times\left(12 / 155^{\circ}\right)$

Express the current $i=22 \sin \left(\omega t+18^{\circ}\right)$ in complex form.