If z= 3 +i 2 , then (z¹⁰¹+i¹⁰³ )¹⁰⁵=

Step-by-step solution

We have, z= 3 +i 2 z= 3 2 + 1 2 i z= 6 +i 6 z=e^ i 6 Now, z¹⁰¹=e^ i ( 101 6 ) =e^ i 16 e^ i 5 6 = - 3 2 + i 2 and i¹⁰³=i¹⁰⁰ i^3=i^3=-i Now, aligned (z¹⁰¹+i¹⁰³ )¹⁰⁵= (- 3 2 + i 2 )-i ¹⁰⁵ & = & [- ( 3 2 + i 2 ) ]¹⁰⁵=(-z)¹⁰⁵ = & - (e^ i 6 )¹⁰⁵=-e^ i 17 e^ i 3 6 = (e^ i 6 )^3=z^3 aligned