Exam 21: Complex Numbers

Multiply: $\left(4.5 e^{j 1.3}\right)\left(8.2 e^{j 0.4}\right)$

Write the conjugate of $-6-j 9$ .

Write as a complex number in rectangular form: $\sqrt{-3}-3$

Combine and simplify: $\left(\frac{1}{3}-\frac{j}{2}\right)+\left(\frac{1}{6}-\frac{j}{4}\right)$

Combine the vectors: $31.2 / \underline{285^{\circ}}-47.9 / \underline{40^{\circ}}$

Express this complex number in exponential form: $\frac{\pi}{3 / \underline{3}}$

Combine the vectors: $8.5 \angle 102^{\circ}+3.2 \angle 18^{\circ}$

Divide and simplify: $\frac{4+\sqrt{-25}}{2-\sqrt{-16}}$

Graph this complex number: 6 - j9

Graph this complex number: $-4+j 7$

Multiply and simplify: $(6-j 4)(5+j 2)$

Divide the vectors: $\left[9\left(\cos 35^{\circ}+j \sin 35^{\circ}\right)\right] \div\left[3\left(\cos 15^{\circ}+j \sin 15^{\circ}\right)\right]$ . Write your answer in polar form.

Express in sinusoidal from: $\mathrm{I}=32.5 / \underline{75^{\circ}}$

Multiply the vectors: $3\left(\cos 35^{\circ}+j \sin 35^{\circ}\right) \times 7\left(\cos 15^{\circ}+j \sin 15^{\circ}\right)$

Evaluate: $\sqrt[4]{16 / \underline{56^{\circ}}}$