A complex number in polar form

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Question from roland:

write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3 - 4i.

Hi Roland,

First use Pythagoras' Theorem to find the |z|, the modulus of z where z = 3 - 4i and then

z = |z| (3/|z| - 4/|z| i)

so p + q i = 3/|z| - 4/|z| i

What remains is to find the argument of z. Since 3 - 4 i is in the 4^th quadrant the argument must be between 270 and 360 degrees. Use this fact and he inverse tangent function to determine the argument of z.

complex plane

Harley

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