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Algebra Level 2

What is a solution to x 2 = i x^2 = i ?

Notation: i = − 1 i=\sqrt{-1} denotes the imaginary unit .

1 3 ( 1 + 2 i ) \frac 1{\sqrt 3} (1 +2i) 1 2 ( 1 + i ) \frac 1{\sqrt 2}(1 + i) There is no solution. i 2 ( 1 + 2 6 i ) \frac i{\sqrt 2} \left(1+ \frac {\sqrt 2}6i\right)

Leafy Li by Leafy Li , 30, USA

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1 solution

X X
Jun 30, 2018

i 1 2 = ( e i π 2 ) 1 2 = e i π 4 = cos ⁡ π 4 + i sin ⁡ π 4 = 1 2 ( 1 + i ) i^{\frac12}=(e^{\frac{i\pi}2})^{\frac12}=e^{\frac{i\pi}4}=\cos\frac{\pi}4+i\sin\frac{\pi}4=\frac1{\sqrt2}(1+i)

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