SOLUTION: Hi, I am stuggling very much on these two questions on complex numbers. If you can help, it would be very much appreciated. Thank you! Directions: In these questions exact value

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi, I am stuggling very much on these two questions on complex numbers. If you can help, it would be very much appreciated. Thank you! Directions: In these questions exact value      Log On


   

Question 396290: Hi, I am stuggling very much on these two questions on complex numbers. If you can help, it would be very much appreciated. Thank you!
Directions: In these questions exact values for θ are to be used and answers are to be expressed as a radical.
1. If z=10(cos225°+i*sin225°) in trigonometric form find z in standard form.
2. If z=6sqrt(3)(cos330°+i*sin330°) in trigonometric form find z in standard form.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'm guessing that what you're really having
problems with is trig. Do you have a solid foundation
in trig? Can you easily convert cos 225 degrees to
an expression with radicals?
225+=+180+%2B+45 degrees, so you have a vector in
the 3rd quadrant where the cosine and sine are both negative
cos%28225%29+=+-+1%2Fsqrt%282%29
sin%28225%29+=+-+1%2Fsqrt%282%29
(1)
z+=+10%2A%28-1%2Fsqrt%282%29+-+i%2A%281%2Fsqrt%282%29%29%29
z+=+%2810%2Fsqrt%282%29%29%2A%28-1+-+i%29
Multiply top and bottom by sqrt%282%29
z+=+5%2Asqrt%282%29%2A%28-1+-+i%29
------------------------------
Note also that
cos%28330%29+=+cos%28360+-+30%29
So the angle is in the 4th quadrant and makes
an angle of 30 with the positive real axis.
The cosine is positive and the sine is negative
cos%28330%29+=+sqrt%283%29%2F2
sin%28330%29+=+-1%2F2
You can finish as I did in (1)