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How do you find a trigonometric form of a complex number?

1 Answer

Feb 22, 2015

Let #z=x+iy# a complex number in algebraic form.

#z=r(cosphi+isinphi)# is its trigonometric form, where:

#r=sqrt(x^2+y^2)# is the modulus of the number and

if #x>0#

#phi=arctan(y/x)# ,

if #x<0#

#phi=arctan(y/x)+pi#,

if #x=0# and #y>0#

#phi=pi/2#,

if #x=0# and #y<0#

#phi=3/2pi#

if #x=y=0#

It's all zero!

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