Square root of a complex number

[Nipon Waiyaworn]

if a is a complex number then sqrt(a^2)=?
Is it is similar to Real Number?
Help me please

 

[Orodruin]

The square root of a complex number ##z## is a complex number ##w## such that ##w^2 = z##. Note that the square root function has two branches, or in other words, there are two possibilites to choose ##w##. ##\sqrt{z^2}=\pm z## depending on the chosen branch and ##z##.

 

[jedishrfu]

Here's an example:

http://www.qc.edu.hk/math/Advanced%20Level/Finding%20the%20square%20root%20of%20a%20complex%20number.htm

 

[Nipon Waiyaworn]

The square root of a complex number ##z## is a complex number ##w## such that ##w^2 = z##. Note that the square root function has two branches, or in other words, there are two possibilites to choose ##w##. ##\sqrt{z^2}=\pm z## depending on the chosen branch and ##z##.

Thanks a lot

 

[Nipon Waiyaworn]

Here's an example:

http://www.qc.edu.hk/math/Advanced%20Level/Finding%20the%20square%20root%20of%20a%20complex%20number.htm

Thanks a lot

 

[WWGD]

Maybe using the polar form would help: ## a=re^{i\theta} ; a^2 =r^2e^{i2\theta} ## . Then its square root , as Orodruin said, is ## \pm re^{i\theta} ## , although if you are working within a branch to start with ## 2\theta ## may not fall within the branch.