Question

Given w=2+2i and v=−5√3+5i,

vw^2 can be expressed as r*(cos(α∘)+i*sin(α∘)),

where r is a real number and 0≤α≤360. What is the value of r+α?

Answer 1

i found
-40i(sqrt(3)-i)
-80i(1/2sqrt(3) -i)
80(1-i*sqrt(3)/2)

then i found that r= 80 and α is -120∘

but r+a must be positive integer

where is the wrong one

Answer 2

vw^2 = (2√2,45°)(2,150°)^2
= (2√2,45°)(4,300°)
= (8√2,345°)