If [z = 3 2 + i 2( i = - 1 )], then (1 + iz + z5 + iz8)9 is equal to :

Question

If $$z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right)$$,

then (1 + iz + z5 + iz8)9 is equal to :

Accepted Answer

$$z = {{\sqrt 3 } \over 2} + {i \over 2}$$

$$ \Rightarrow $$ z = $$\cos {\pi  \over 6}$$ + i $$\sin {\pi  \over 6}$$

$$ \Rightarrow $$ z = $${e^{i{\pi  \over 6}}}$$

Solutions · 1