Express the polar form of zw, z/w and 1/z where; z=4√3-4i, w=8i

Answer 1

z = 4√3-4i
w = 8i = 0 + 8i

zw = (4√3-4i)(8i)
= 32√3i - 32i^2
= 32 + 32√3i

z/w = (4√3 - 4i)/(8i) * i/i
= (4√3i - 4i^2) / -8
= -1/2 - √3/2 i

1/z = 1/(4√3 - 4i) * (4√3 + 4i)/(4√3 + 4i)
= (4√3 + 4i)/(48 - 16i^2)
= (4√3 - 4i)/64
= (√3 - i)/16 or √3/16 - 1/16 i