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Simplify (1 + i√3)^6

 Jul 10, 2023
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We can write [(1 + \sqrt{-3})^6 = (1 + i \sqrt{3})^6.]Let z=1+i3​. Then z2=1+2i3​+3=4i3​, so z3=−3i, and \begin{align*} z^6 &= z^3 z^3 \ &= -3i(-3i) \ &= 9. \end{align*}

Therefore, (1+i*sqrt(3))^6 = 9 ​.

 Jul 10, 2023

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