What is the polar form of the complex number 6-4i ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A complex number a + ib can be written in the polar form r*cis A where r is the absolute value of the complex number or sqrt (a^2 + b^2) and A  = arc tan (y/x)

Here we have z = 6 - 4i.

r = sqrt (6^2 + 4^2) = sqrt (36 + 16) = 2*sqrt 13

A = arc tan (-4/6) = arc tan (-2/3) = -33.69 degrees

The polar form of the complex number is 2*sqrt 13 cis -33.69

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