SOLUTION: Express the complex number in trigonometric form. 6 - 6i Please write the answer in radians, andshow work THANK YOU

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Question 1090711: Express the complex number in trigonometric form.
6 - 6i
Please write the answer in radians, andshow work
THANK YOU
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

This is the trigonometric form of a complex number where abs%28z%29is the modulus and theta is the angle created on the complex plane.
z=a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29
The modulus of a complex number is the distance from the origin on the complex plane.
abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29 where z=a%2Bbi
Substitute the actual values of a=6 and b=-6
.
abs%28z%29=sqrt%286%5E2%2B%28-6%29%5E2%29
abs%28z%29=sqrt%2836%2B36%29
abs%28z%29=sqrt%282%2A36%29
abs%28z%29=6sqrt%282%29
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
theta=tan%5E-1%28-6%2F6%29
Since inverse tangent of -6%2F6 produces an angle in the fourth quadrant, the value of the angle is+-pi%2F4
.
theta=+-pi%2F4
Substitute the values of theta=+-pi%2F4 and abs%28z%29=6sqrt%282%29 in
a%2Bbi=abs%28z%29%28cos%28theta%29%2Bi%2Asin%28theta%29%29
.
6-6i=6sqrt%282%29%28cos%28+-pi%2F4%29%2Bi%2Asin%28+-pi%2F4%29%29