$\mathrm{a}+\mathrm{ib}$ form of $\left(\frac{1}{3}+3 \mathrm{i}\right)^2$ is

Question

Professor PC Thomas Classes · Answer

$\left(\frac{1}{3} + 3i\right)^2 = \frac{1}{9} + 2\left(\frac{1}{3}\right)(3i) + 9i^2 = \frac{1}{9} + 2i - 9 = -\frac{80}{9} + 2i$.