How to solve a fraction of imaginary numbers? [closed]

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I have the following equation.

$a = \frac{(1/2) - (3/2)i}{(3/2) + (3/2)i}$

The solution says that $a^2 = 5/9$.

I don't know how I can perform the steps, could I get some feedback?

Thanks!

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1 Answer

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Hint:

Multiply numerator and denominator by the complex conjugate of the latter first:$$\frac{\frac12-\frac32 i}{\frac32+\frac32i}=\frac{\frac12}{\frac32}\frac{1-3i}{1+i}=\frac13\frac{(1-3i)(1-i)}{(1+i)(1-i)}$$Can you proceed?

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