Complex Numbers in Rectangular and Polar Form

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Every complex number written in rectangular form

x+yi

has a unique polar form

ρ(cosθ+isinθ

) up to an integer multiple of

2π

in its argument. The principal value of the argument is normally taken to be in the interval

-π<argz≤π

. However, this creates a discontinuity as

z

moves across the negative real axis.