SOLUTION: Express the complex number in trigonometric form. -2 + 2 square root of three i

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Question 1134030: Express the complex number in trigonometric form.
-2 + 2 square root of three i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-2+%2B+2sqrt%283%29%2A+i+
z+=+a+%2B+i+b+
z=-2+%2B+2sqrt%283%29%2A+i => a=+-2, b=2sqrt%283%29

trigonometric form:
z=+r+%28+cos%28theta%29+%2B+i+sin%28theta%29+%29

where:
r+=+sqrt%28a%5E2+%2B+b%5E2%29 and tan%28theta%29+=+b+%2F+a
r+=+sqrt%28%28-2%29%5E2+%2B+%282sqrt%283%29%29%5E2%29
r+=+sqrt%284+%2B+4%283%29%29
r+=+sqrt%284+%2B+12%29
r+=+sqrt%2816%29
r+=+4

tan%28theta%29+=+2sqrt%283%29+%2F+-2
tan%28theta%29+=+-sqrt%283%29
theta=pi%2Btan%5E-1%28-sqrt%283%29%29
theta=+%282+pi%29%2F3
theta=120°
then,
z=+4+%28+cos%28120%29+%2B+i%2A+sin%28120%29+%29