Question Number 32203 by rahul 19 last updated on 21/Mar/18
![Number of solutions of the equation z^3 +(([3(z^− )^2 ])/(∣z∣))=0 where z is a complex no.](https://www.tinkutara.com/question/Q32203.png)
$$\boldsymbol{{N}}{umber}\:{of}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$${z}^{\mathrm{3}} +\frac{\left[\mathrm{3}\left(\overset{−} {{z}}\right)^{\mathrm{2}} \right]}{\mid{z}\mid}=\mathrm{0}\:{where}\:{z}\:{is}\:{a}\:{complex}\:{no}. \\ $$
Commented by rahul 19 last updated on 21/Mar/18
Commented by rahul 19 last updated on 21/Mar/18
$${pls}\:{explain}\:{this}\:''\mathrm{5}\:{distinct}\:{values}\:{of}\theta''. \\ $$$${and}\:{why}\:{r}\neq−\sqrt{\mathrm{3}}? \\ $$
Commented by MJS last updated on 21/Mar/18
$${a}+{b}\mathrm{i} \\ $$$${r}=\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\geqq\mathrm{0} \\ $$
Commented by MJS last updated on 21/Mar/18
$$ \\ $$$${e}^{\mathrm{5}{i}\theta} =−\mathrm{1} \\ $$$$\left({e}^{{i}\theta} \right)^{\mathrm{5}} =−\mathrm{1} \\ $$$${x}^{{n}} ={c} \\ $$$$\mathrm{has}\:\mathrm{got}\:\mathrm{5}\:\mathrm{solutions}\: \\ $$
Commented by rahul 19 last updated on 21/Mar/18
$${thank}\:{u}\:{sir}. \\ $$