Question

Express
$(cos2\theta +isin2\theta {)}^{-5}$ $(cos3\theta -isin3\theta {)}^6$ $(sin\theta -icos\theta {)}^3$
in the form of A+iB is

• A. (cos25 + isin25)
• B. i(cos25 + isin25)
• C. i(cos25 - isin25)
• D. (cos25 - isin25)

Answer 1

The correct option is C

i(cos25 - isin25)

sin$\theta$-icos$\theta$= -$i^2$ sin$\theta$-icos$\theta$ = -i(cos$\theta$+isin$\theta$)

Given expression is

$(-i{)}^3$ [cos(-10$\theta$-18$\theta$+3$\theta$+isin(-25$\theta$)]

=i(cos25$\theta$ - isin 25 $\theta$ ] .