Question Number 36676 by tawa tawa last updated on 04/Jun/18
$$\mathrm{if}\:\:\mathrm{z}\:=\:−\:\mathrm{27},\:\:\mathrm{find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{z}\:\mathrm{in}\:\mathrm{complex}\:\mathrm{plain} \\ $$
Commented by abdo mathsup 649 cc last updated on 04/Jun/18
$${the}\:{roots}\:{are}?{the}\:{comlex}\:{z}\:/\:{z}^{\mathrm{2}} \:=−\mathrm{27}\:=\left({i}\sqrt{\mathrm{27}}\right)^{\mathrm{2}} \:{so} \\ $$$${the}\:{roots}\:{are}\:{i}\sqrt{\mathrm{27}}\:\:{and}\:−{i}\sqrt{\mathrm{27}}\:. \\ $$
Commented by tawa tawa last updated on 04/Jun/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$
Commented by abdo.msup.com last updated on 05/Jun/18
$${a}\:{lots}\:{of}\:{thanks}\:{sir}\:{Tawa}\:{Tawa}... \\ $$
Answered by Rasheed.Sindhi last updated on 04/Jun/18
$$\mathrm{Let}\:\mathrm{z}=\mathrm{x}+\mathrm{iy} \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{iy}=−\mathrm{27} \\ $$$$\mathrm{x}=−\mathrm{27},\mathrm{y}=\mathrm{0} \\ $$$$\left(−\mathrm{27},\mathrm{0}\right)\:\left(\mathrm{single}\:\mathrm{root}\right) \\ $$
Commented by tawa tawa last updated on 05/Jun/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$