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# Imaginary Number Equation

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Solve the following equation in full detail:

$$x^2 = 2i$$

Aug 5, 2020

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(a+bi)^2=2i

then you expand to $$\left(a^2-b^2\right)+2iab=2i$$

$$\left(a^2-b^2\right)+2iab=0+2i$$

then, let's write is as system of equations: (I assume you know what it is)

$$\begin{bmatrix}a^2-b^2=0\\ 2ab=2\end{bmatrix}$$

So, $$x=1+i,\:x=-1-i$$