Is the complex square root of z^2 = +- z I think it is, since either −z or +z satisfies the definition sqrt(z^2)= e^( 1/2 log(z)^2) but I just wanted to make sure.

Sonia Elliott

Sonia Elliott

Answered question

2022-10-23

Is the complex square root of z 2 = ± z?
Is z 2 = ± z, for z complex?
I think it is, since either z or + z satisfies the definition
z 2 = e 1 2 log ( z ) 2
but I just wanted to make sure. It's a bit tricky going from the positive square to the complex square root.
Thanks,

Answer & Explanation

aitorarjolia

aitorarjolia

Beginner2022-10-24Added 11 answers

The notation x is usually avoided except when referring to the non-negative square root of a non-negative real number, because otherwise it's ambiguous. In C it is better to refer to "a square root" not "the square root". You will also come across the phrase " x is an nth root of 1" (when it is understood that n is a positive integer) which means that x n = 1 and does not specify or restrict which of n possible values x might be.

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