jee-main 2016 Q62

jee-main · India · 10apr Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers

Let $z = 1 + a i$, be a complex number, $a > 0$, such that $z ^ { 3 }$ is a real number. Then, the sum $1 + z + z ^ { 2 } + \ldots + z ^ { 11 }$ is equal to :
(1) $1365 \sqrt { 3 } i$
(2) $- 1365 \sqrt { 3 } i$
(3) $- 1250 \sqrt { 3 } i$
(4) $1250 \sqrt { 3 } i$

Let $z = 1 + a i$, be a complex number, $a > 0$, such that $z ^ { 3 }$ is a real number. Then, the sum $1 + z + z ^ { 2 } + \ldots + z ^ { 11 }$ is equal to :\\
(1) $1365 \sqrt { 3 } i$\\
(2) $- 1365 \sqrt { 3 } i$\\
(3) $- 1250 \sqrt { 3 } i$\\
(4) $1250 \sqrt { 3 } i$

Paper Questions

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