Question

if z=7-i/3-4i then find the value of z^14

Answer 1

z=7-13i/3
|z|=root(49+169/9)
|z|=root(610/9)
no we'll find the argument
tan theta= (-13/3)/7
theta= -31.7 degrees
or theta=-0.552 radians
so
z=|z|e^(i*(-0.552))
z^14= (610/9)^7e^(i*(-0.552*7)
z^14=(610/9)^7 e^(i(-3.85))