1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form:
a. 5 – 8i
Answer = Sqrt{89} ( cos (1.01219701) + i sin ( 1.01219701))
b. –1 – i
answer = Sqrt2 (cos (5pi/4) + i sin (5pi/4))
c. –5 + 12i
answer = 13 (cos ( 4.31759786068493) + i sin ( 4.31759786068493))
d. 1 + sqrt{3}i
answer = 2 ( cos (pi/3) + i sin (pi/3))
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2 answers

all look good, but I'm curious why you had negative angles for (a) annd (c).
For (a) I could see it, because the angle is greater than pi
For (c) I would have added 2pi to get an angle less than pi, since the angle is in QII. 👍
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answered by Steve 
I think he/she has a negative angle for a) by entering the data into a calculator and simply blindly accepting the answer the calculator gives.
Remember the calculator is programmed to give the closest angle to zero.
so tan^1 (8/5) = 1.012....
I would take 2π  1.012.... 👍
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answered by Reiny
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