Square root of a complex number

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  • Thread starter Nipon Waiyaworn
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  • #1
Nipon Waiyaworn
if a is a complex number then sqrt(a^2)=?
Is it is similar to Real Number?
Help me please
 

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  • #2
Orodruin
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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##.
 
  • #4
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
 
  • #6
WWGD
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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.
 

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