Question

Find square root of $0+3i$

Answer 1

$\sqrt{0+3i}=\sqrt{3i}$

$\sqrt{3i}=\sqrt{3}\times i^{1/2}$

As we know that $i=e^{i\frac{\pi }{2}}$

So $\sqrt{3i}=\sqrt{3}(e^{i\frac{\pi }{2}}{)}^{1/2}=\sqrt{3}(e^{i\frac{\pi }{4}})=\sqrt{\frac{3}{2}}(1+i)$