Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.
A) $32 \sqrt { 2 } i$
B) $- 32 \sqrt { 2 } i$
C) $1024 \sqrt { 2 } i$
D) $- 32 \sqrt { 2 }$
E) The expression cannot be simplified.

Question

Quizplus · Accepted Answer

$(\sqrt{-2})^{11} = (\sqrt{2}i)^{11} = (\sqrt{2})^{11} \cdot i^{11} = 2^{5.5} \cdot i^{11} = 32\sqrt{2} \cdot i^{11} = 32\sqrt{2} \cdot i^{(10+1)} = 32\sqrt{2} \cdot i^{10} \cdot i = 32\sqrt{2} \cdot (-1) = -32\sqrt{2}i$.

Simplify (−2)11( \sqrt { - 2 } ) ^ { 11 }(−2​)11

Simplify $( \sqrt { - 2 } ) ^ { 11 }$