Given that ${{\left| \frac{2\mathbf{i}-{{z}^{*}}}{z}-1 \right|}^{2}}+z=-\mathbf{i}$, find $z$ in the

Question

Given that ${{\left| \frac{2\mathbf{i}-{{z}^{*}}}{z}-1 \right|}^{2}}+z=-\mathbf{i}$, find $z$ in the form $x+\mathbf{i}y$. State the exact values of $\left| z \right|$ and $\arg \left( z \right)$. [5]

Accepted Answer

$z = -4 - i$, $|z| = \sqrt{17}$, $\arg z = \tan^{-1}\left(\frac{1}{4}\right) - \pi$

RI Complex Numbers Tutorial Q4

RI Complex Numbers Tutorial Q4

Video Solution:

Solution:

Solution locked