QJEEM19Ma35f3: JEE Main 2019 Mathematics - Class 11 JEEM19Ma35f3 Solution: If , then (1 + iz + z 5 + iz 8 ) 9 is equal to :

Question

Verified Solution • 2025–26 Session moderate

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}}}

Step-by-Step Verified Solution