Given that $z=(b+i)^2$, where $b$ is real and positive, find the exact value of $b$

Question

Given that $z=(b+i)^2$, where $b$ is real and positive, find the exact value of $b$ when $\arg(z)=60{}^\circ$.

Accepted Answer

$b = \sqrt{3}$.

Connecting squaring and argument of a complex number