simply this equation

Question

8(cos90°+isin90°)÷4(cos30°+isin30°)

Answer 1

Use De Moivre's Theorem a couple times

cos60= 1/2, sin60= sqr3/2

8(cos90+isin90)/4(cos30+isin30) = 8(cos30+isin30)^3/4cos30+isin30) = 2(cos30+isin30)^2

= 2(cos60+isin60) =2(1/2 +isqr3/2) = 1+(1/2)(sqr3)i = about 1+0.866i