91Ó°ÊÓ

perform the indicated operations, expressing all answers in the form \(a+b j\) $$\left(2 j^{2}-3 j^{3}+2 j^{4}-2 j^{5}\right)^{6}$$

Use DeMoivre's theorem to find all the indicated roots. Be sure to find all roots. The three cube roots of \(27\left(\cos 120^{\circ}+j \sin 120^{\circ}\right)\)

Solve the given problems. For \(x+y j,\) what is the argument if \(x=y<0 ?\)

Perform the indicated vector operations graphically on the complex number \(2+4 j\) Graph the number, the number multiplied by \(j\), the number multiplied by \(j^{2},\) and the number multiplied by \(j^{3}\) on the same graph. Describe the result of multiplying a complex number by \(j\)

Perform the indicated operations and simplify each complex number to its rectangular form. $$5-2 \sqrt{25 j^{2}}$$

evaluate each expression on a calculator. Express answers in the form \(a+b j\) $$\left(3 j^{9}-5 j^{3}\right)\left(4 j^{6}-6 j^{8}\right)$$

Perform the indicated vector additions graphically. Check them algebraically. Two ropes hold a boat at a dock. The tensions in the ropes can be represented by \(40+10 j\) lb and \(50-25 j\) lb. Find the resultant force.

Use DeMoivre's theorem to find all the indicated roots. Be sure to find all roots. The three cube roots of \(3-4 j\)

Perform the indicated operations and simplify each complex number to its rectangular form. $$2 j^{2}+3 j$$

Perform the indicated operations. The impedance in an antenna circuit is \(3.75+1.10 j\) ohms. Write this in exponential form and find the magnitude of the impedance.