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Question Number 196893 by hardmath last updated on 02/Sep/23

Answered by Rasheed.Sindhi last updated on 02/Sep/23

$$x=\sqrt{(-1+i)+\sqrt{(-1+i)+\sqrt{...}}}$$$$x=\sqrt{(-1+i)+x}$$$$x^2=(-1+i)+x$$$$x^2-x+1-i=0$$$$x=\frac{1\pm \sqrt{1-4(1-i)}}{2}$$$$x=\frac{1\pm \sqrt{-3+4i}}{2}$$$$=\frac{1\pm (1+2i)}{2}$$$$=\frac{2+2i}{2},\frac{-2i}{2}$$$$=1+i,-i$$

Commented by BaliramKumar last updated on 02/Sep/23

$$\sqrt{-3+4i}=1+2i$$

Commented by Rasheed.Sindhi last updated on 02/Sep/23

$$\mathcal{T}han\mathcal{X}!Goingtoeditmyanswer.$$

Commented by hardmath last updated on 05/Sep/23

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{professor}$$

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