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Question Number 54466 by 05051993 last updated on 04/Feb/19

((6+(√((6)^2 −4(1)(10))))/2)

$$\frac{\mathrm{6}+\sqrt{\left(\mathrm{6}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{10}\right)}}{\mathrm{2}} \\ $$$$ \\ $$

Commented by Tawa1 last updated on 04/Feb/19

= ((6 + (√(36 − 40)))/2)  = ((6 + (√(− 4)))/2)  = ((6 + (√(− 1 × 4)))/2)  = ((6 + (√(− 1)) × (√4))/2)                        Where,     (√(− 1))  =  i  = ((6 + 2i)/2)  = (6/2) + ((2i)/2)  = 3 + i

$$=\:\frac{\mathrm{6}\:+\:\sqrt{\mathrm{36}\:−\:\mathrm{40}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{4}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{1}\:×\:\mathrm{4}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{1}}\:×\:\sqrt{\mathrm{4}}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Where},\:\:\:\:\:\sqrt{−\:\mathrm{1}}\:\:=\:\:\mathrm{i} \\ $$$$=\:\frac{\mathrm{6}\:+\:\mathrm{2i}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}}{\mathrm{2}}\:+\:\frac{\mathrm{2i}}{\mathrm{2}} \\ $$$$=\:\mathrm{3}\:+\:\mathrm{i} \\ $$

Answered by Prithwish sen last updated on 04/Feb/19

= 3+i (where i= (√(−1))

$$=\:\mathrm{3}+\mathrm{i}\:\left(\mathrm{where}\:\mathrm{i}=\:\sqrt{−\mathrm{1}}\right. \\ $$

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