Find the exact square roots of the complex number $6\mathbf{i}$.

Hence, solve the quadratic equation $z^{2} + 2\mathbf{i}z - 1 - 6\mathbf{i} = 0$.

Question

Find the exact square roots of the complex number $6\mathbf{i}$. Hence, solve the quadratic equation $z^{2} + 2\mathbf{i}z - 1 - 6\mathbf{i} = 0$.

Accepted Answer

$z=\sqrt{3}+\sqrt{3}\mathbf{i}$ or $-\sqrt{3}-\sqrt{3}\mathbf{i}$; $z=\sqrt{3}+(\sqrt{3}-1)\mathbf{i}$ or $-\sqrt{3}-(\sqrt{3}+1)\mathbf{i}$

Complex Numbers - Finding Square Roots of Complex Numbers Algebraically