Answer
a.) $4\sqrt{2} * e^{j*\frac{\pi}{4}} $
b.) $5*e^{j*2.2143}$
c.)$\sqrt{10} *e^{-j*1.8925}$
Work Step by Step
For each iteration, find the magnitude of each complex number using $\sqrt{a^2 +b^2}$ and find the angle using arctan(b/a).
a.) $\sqrt{16+16}= 4*\sqrt{2}$
$arctan(1) = \pi/4 $ rad
a=$4\sqrt{2}e^{j\frac{\pi}{4}}$
b.) $\sqrt{9+16} = 5$
$arctan(-4/3) = -0.9273 + \pi = 2.2143$ rad
b=$5*e^{j*2.2143}$
c.) $\sqrt{1+9} = \sqrt{10}$
$arctan(3/1) = 1.249 - \pi = -1.8925$ rad
c = $\sqrt{10} *e^{-j*1.8925}$
