Please Solve:

a^2-(i^2)(b^2) =a^2 b^2

It should be   ${\mathrm{a}}^2 - \left({\mathrm{i}}^2\right)\left({\mathrm{b}}^2\right) = {\mathrm{a}}^2 + {\mathrm{b}}^2$

Let a = rcos x  , b = rsin x

Now, LHS = (a - ib ) (a +ib) = (rcos x - i rsinx)(rcosx + irsin x)
    =${\mathrm{r}}^2({\cos }^2\mathrm{x} + {\sin }^2\mathrm{x}) = {\mathrm{r}}^2$

RHS

$$\begin{gathered} {\mathrm{a}}^2 + {\mathrm{b}}^2 \\ = {\mathrm{r}}^2{\cos }^2\mathrm{x} + {\mathrm{r}}^2{\sin }^2\mathrm{x} \\ ={\mathrm{r}}^2 \end{gathered}$$