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Polar Form


The polar form of a nonzero complex number z=x+iy expresses z in terms of the polar coordinates (r,theta) of the point (x,y) as

 z=r(costheta+isintheta)=re^(itheta),

where r=|z|=sqrt(x^2+y^2) is the complex modulus and theta=argz is a complex argument. The latter is defined only modulo 2pi; choosing a specified interval gives a principal argument. In polar form, complex multiplication multiplies complex moduli and adds complex arguments.


See also

Complex Argument, Complex Modulus, Euler Formula, Polar Coordinates

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References

Churchill, R. V. and Brown, J. W. Complex Variables and Applications, 5th ed. New York: McGraw-Hill, 1990.

Cite this as:

Weisstein, Eric W. "Polar Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PolarForm.html

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