Write $\displaystyle z=i-1$ in form of $\displaystyle {re}^{iv}$
It's a math exercise! And it is asking you to change a complex number written in Cartesian form to its "polar form". The simplest way to do that is to graph i- 1 as (-1, 1) (using the x-axis as the real axis, the y-axis as the imaginary axis). Now, your "r" is the distance from (0, 0) to (-1, 1) and your "v" is the angle the line from (0,0) to (-1, 1) makes with the positive real (x) axis. Can you calculate those?
The principle value of the argument of a complex number $\displaystyle z=a+bi$ not on any axis is found by the following.
$\displaystyle Arg(z) = \left\{ {\begin{array}{rl}
{\arctan \left( {\frac{b}
{a}} \right),} & {a > 0} \\
{\arctan \left( {\frac{b}
{a}} \right) + \pi ,} & {a < 0\;\& \,b > 0} \\ \\
{\arctan \left( {\frac{b}
{a}} \right) - \pi ,} & {a < 0\;\& \,b < \pi } \\
\end{array} } \right.$
Please note that $\displaystyle \mathif{i}-1=-1+\mathif{i}$ and there $\displaystyle a=-1~\&~b=1$.