Question Number 22769 by Bruce Lee last updated on 22/Oct/17
$$\boldsymbol{\mathrm{write}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{geometry}}\:\boldsymbol{\mathrm{form}} \\ $$$$\:\frac{\mathrm{3}}{\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{5}}\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{plz}}\: \\ $$
Answered by $@ty@m last updated on 22/Oct/17
$${Let}\:\frac{\mathrm{3}}{\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{5}}\boldsymbol{\mathrm{i}}={r}\mathrm{cos}\:\theta+{i}.{r}\mathrm{sin}\:\theta \\ $$$$\Rightarrow{r}\mathrm{cos}\:\theta=\frac{\mathrm{3}}{\mathrm{5}}\:\&\:{r}\mathrm{sin}\:\theta=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\Rightarrow{r}=\mathrm{1}\:\&\:\theta=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\therefore\frac{\mathrm{3}}{\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{5}}\boldsymbol{\mathrm{i}}=\mathrm{cos}\:\theta+{i}.\mathrm{sin}\:\theta \\ $$$${where}\:\theta=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}} \\ $$