Question

Find the modulus of the following complex numbers: (2+i)/(4i + (1+i) whole square.

Answer 1

$$\begin{gathered} \mathrm{Assuming}\mathrm{your}\mathrm{question}\mathrm{as}, \\ \frac{2+\mathrm{i}}{4\mathrm{i}+{\left(1+\mathrm{i}\right)}^2}=\frac{2+\mathrm{i}}{4\mathrm{i}+1+{\mathrm{i}}^2+2\mathrm{i}}=\frac{2+\mathrm{i}}{4\mathrm{i}+1-1+2\mathrm{i}}=\frac{2+\mathrm{i}}{6\mathrm{i}} \\ =\frac{2+\mathrm{i}}{6\mathrm{i}}\times \frac{\mathrm{i}}{\mathrm{i}}=\frac{2\mathrm{i}}{-6}-\frac{1}{-6}=\frac{1}{6}-\frac{\mathrm{i}}{3} \\ \mathrm{So}\left|\frac{1}{6}-\frac{\mathrm{i}}{3}\right|=\sqrt{{\left(\frac{1}{6}\right)}^2+{\left(\frac{-1}{3}\right)}^2}=\sqrt{\frac{1}{36}+\frac{1}{9}}=\sqrt{\frac{5}{36}}=\frac{\sqrt{5}}{6} \end{gathered}$$