Let z be a complex number such that

Question

z=2(cos3∘+icos87∘).

Then z^6 can be expressed as r(sinα∘+icosα∘),

where r is a real number and 0≤α≤90. What is the value of r+α?

Answer 1

i found that r = 64 and α is 18; any one can clarify this ?

Answer 2

You fell into the trap

z^6 = 64 cis18° = 64(cos18° + i sin18°)

and it is thus 64(sin72° + i cos72°)

Answer 3

waaaaaa thx steve