91Ó°ÊÓ

The polar form of a complex number is: $$ z=r e^{i \theta} $$ where $$ r e^{i \theta}=r(\cos (\theta)+i \sin (\theta)) $$ Octave can determine the magnitude (modulus) \(r\) and angle (argument) \(\theta\) of a complex number \(z\) using the commands abs(z) and angle(z), respectively. (a) Write the polar form of \(z_{1}=3-7 i\) and \(z_{2}=1+5 i\) (b) Find \(z_{1} z_{2}\) in both polar and \(a+b i\) form. How are the magnitudes and angles of each number related to the magnitude and angle of the product? (c) Find \(z_{1} / z_{2}\) in both polar and \(a+b i\) form. How are the magnitudes and angles of each number related to the magnitude and angle of the quotient?