Question

express the complex number in standed form a+ib i⁹⁹

Answer 1

Dear Student ,

$$\begin{gathered} {\mathrm{i}}^{99}={\mathrm{i}}^{96}.{\mathrm{i}}^3 \\ ={\left({\mathrm{i}}^4\right)}^{24}.\left(-\mathrm{i}\right)\left(\mathrm{Since}{\mathrm{i}}^3=-\mathrm{i}\right) \\ ={\left(1\right)}^{24}.\left(-\mathrm{i}\right)\left(\mathrm{Since}{\mathrm{i}}^4=1\right) \\ =-\mathrm{i} \\ =0-\mathrm{i}\mathrm{ANS}... \end{gathered}$$