91Ó°ÊÓ

Perform the indicated operations and simplify each complex number to its rectangular form. $$j^{3}-6$$

evaluate each expression on a calculator. Express answers in the form \(a+b j\) $$\left(5 j-4 j^{2}+3 j^{7}\right)\left(2 j^{12}-j^{13}\right)$$

Perform the indicated vector additions graphically. Check them algebraically. Relative to the air, a plane heads north of west with a velocity that can be represented by \(-480+210 j \mathrm{km} / \mathrm{h}\). The wind is blowing from south of west with a velocity that can be represented by \(60+210 j \mathrm{km} / \mathrm{h} .\) Find the resultant velocity of the plane.

Use DeMoivre's theorem to find all the indicated roots. Be sure to find all roots. The two square roots of \(-5+12 j\)

Perform the indicated operations. The intensity of the signal from a radar microwave signal is \(37.0\left[\cos \left(-65.3^{\circ}\right)+j \sin \left(-65.3^{\circ}\right)\right] \mathrm{V} / \mathrm{m} .\) Write this in exponential form.

evaluate each expression on a calculator. Express answers in the form \(a+b j\) $$\frac{\left(2-j^{3}\right)^{4}}{\left(j^{8}-j^{6}\right)^{3}}+j$$

Use DeMoivre's theorem to find all the indicated roots. Be sure to find all roots. The square roots of \(1+j\)

Perform the indicated operations and simplify each complex number to its rectangular form. $$\sqrt{18}-\sqrt{-8}$$

Perform the indicated operations. In an electric circuit, the admittance is the reciprocal of the impedance. If the impedance is \(2800-1450 j\) ohms in a certain circuit, find the exponential form of the admittance.

Solve the given problems. The voltage of a certain generator is represented by \(2.84-1.06 j \mathrm{kV} .\) Write this voltage in polar form.