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Hi! I've got a question.

There is a nice formula for finding square roots of arbitrary complex numbers z=a+bi:

[itex]\frac{1}{\sqrt{2}}(\epsilon\sqrt{|z|+a}+i\sqrt{|z|-a})[/itex] where

epsilon:=sing(b) if b≠0 or epsilon:=1 if b=0.

I've just looked it up and it's nice to use it to find complex roots of quadratic equations with complex coefficients.

Where does it come from? I mean, squaring shows that it's true but how can one derive it from other facts? Is there a similar formula for n-th roots (not in polar form but analogous to that above)? Any info, links?

There is a nice formula for finding square roots of arbitrary complex numbers z=a+bi:

[itex]\frac{1}{\sqrt{2}}(\epsilon\sqrt{|z|+a}+i\sqrt{|z|-a})[/itex] where

epsilon:=sing(b) if b≠0 or epsilon:=1 if b=0.

I've just looked it up and it's nice to use it to find complex roots of quadratic equations with complex coefficients.

Where does it come from? I mean, squaring shows that it's true but how can one derive it from other facts? Is there a similar formula for n-th roots (not in polar form but analogous to that above)? Any info, links?

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