Express z=(6-2i)(1-3i) in polar form and calculate z^4. Express results in both polar and rectangular form.
Workings: (6-2i)(1-3i) 6-20i-6 0-20i. z^4=(-20i)(-20i)(-20i)(-20i) z^4=0+160000i -> Rectangular Form. Tan theta=y/x Theta=tan^-1(160000/0) Theta=0 r=160000 160000(cos0 + i sin0) -> Polar form.
Is this correct?
You cannot use $$\tan{(\theta)}=\frac{y}{x}$$ when $x=0$. Instead you need to know that the principal argument of $i$ is $$\arg{(i)}=\frac{\pi}{2}$$ You can get this by considering an Argand diagram. Then you have $$160000i=160000(\cos{(\pi/2)}+i\sin{(\pi/2)})$$