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Question

The number of solution of the equation z2+|z|2=0, where ZC is

A
one
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B
two
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C
three
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D
infinitely many
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Solution

The correct option is B two
Let z=reiθ (euler form)
z2+|z|2=r2e2iθ+r2=0
e2iθ+1=0
We know e2iθ=cos2θ+isin2θ=1
cos2θ=1,sin2θ=0
Solutions are θ=π2,π2
So, two solution exist for this equation.

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