Question Number 195446 by sonukgindia last updated on 02/Aug/23
Answered by Frix last updated on 02/Aug/23
$$\sqrt{{a}+{b}\mathrm{i}}=\frac{\sqrt{{a}+\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}}{\:\sqrt{\mathrm{2}}}+\mathrm{sign}\:{b}\:\frac{\sqrt{−{a}+\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}}{\:\sqrt{\mathrm{2}}}\mathrm{i} \\ $$$$\sqrt{−\mathrm{110}+\mathrm{66i}}=\sqrt{\mathrm{11}\left(−\mathrm{5}+\sqrt{\mathrm{34}}\right)}+\mathrm{i}\sqrt{\mathrm{11}\left(\mathrm{5}+\sqrt{\mathrm{34}}\right)} \\ $$