Question

Can anyone help me with this?
Let z = 1+i√3. Find the polar form of z^5

I know it's something like 2(cos ( ) isin( )) but I'm not sure what it is.
is it 2(cosπ + (1/2)isinπ) = z?

Answer 1

first write z in polar form
apply de movries theorem for z^5
u will get the answer
be happy :)

Answer 2

z = 1+i√3
-> x = 1 , y = √3
=> r = √ ( 1^2 + √3^2 ) = 2 ,
sin theta = 1/2 => theta = pi/6
Thus polar form:
z = 2 cis pi/6
z^5 = 32 cis 5 * pi/6