How to use De Moivre's theorem to solve equations?

Question

Can someone please explain to me how to do question 1a? Thanks!

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Answer 1 · 2018-03-02T07:53:11

The solution is #S={i}#

We need

#i^2=-1#

The equation is

#z^2+1=0#

Therefore,

#z^2+1+(color(red)(-1))=0+(color(red)(-1))#

#z^2+0=0+(color(red)(-1))=color(red)(-1)#

#z^2=color(red)(-1)#

#z^2=i^2#

#z=i#