If a- -1-i- 3 2 -b- -1-i- 3 2 then show that a 2 -b and b 2 -a-

a= 1+i√(3)2 ⇒a^2=( 1+i√(3)2)^2 =1+3i^2 2√(3)i4 =1 3 2i√(3)4 = 2 2i√(3)4 = 1 i√(3)2=b b= 1 i√(3)2 ⇒b^2=( 1 i√(3)2)^2 ...

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Complex Numbers

If a= -1+i√...

Question

If $a = \frac{- 1 + i \sqrt{3}}{2}, b = \frac{- 1 - i \sqrt{3}}{2}$ then show that $a^{2} = b$ and $b^{2} = a .$

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