Question Number 54466 by 05051993 last updated on 04/Feb/19
$$\frac{\mathrm{6}+\sqrt{\left(\mathrm{6}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{10}\right)}}{\mathrm{2}} \\ $$$$ \\ $$
Commented by Tawa1 last updated on 04/Feb/19
$$=\:\frac{\mathrm{6}\:+\:\sqrt{\mathrm{36}\:−\:\mathrm{40}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{4}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{1}\:×\:\mathrm{4}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{1}}\:×\:\sqrt{\mathrm{4}}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Where},\:\:\:\:\:\sqrt{−\:\mathrm{1}}\:\:=\:\:\mathrm{i} \\ $$$$=\:\frac{\mathrm{6}\:+\:\mathrm{2i}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}}{\mathrm{2}}\:+\:\frac{\mathrm{2i}}{\mathrm{2}} \\ $$$$=\:\mathrm{3}\:+\:\mathrm{i} \\ $$
Answered by Prithwish sen last updated on 04/Feb/19
$$=\:\mathrm{3}+\mathrm{i}\:\left(\mathrm{where}\:\mathrm{i}=\:\sqrt{−\mathrm{1}}\right. \\ $$