SOLUTION: Write the following numbers in the polar form r(cos(theta)+isin(theta)) 0<(theta)<2pi. Thank you! 1) 4i 2) -4+2i

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Question 616995: Write the following numbers in the polar form r(cos(theta)+isin(theta)) 0<(theta)<2pi. Thank you!
1) 4i
2) -4+2i
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
In general

where the "a" and "b" come from the "a + bi" form of complex numbers.

1) 4i
First we write it in "a + bi" form:
0 + 4i
So the "a" = 0 and the "b" = 4
Putting these values into the formulas:

From our knowledge of special angles we should know what is. The angle between 0 and with a cos of 0 and a sin of 1 is: . So

2) -4+2i
This makes "a" = -4 and "b" = 2. Putting these values into the formulas:

From our knowledge of special angles we should know that none of the special angle values have in them. So is not a special angle. So we will need our calculators to find . First we get decimals for cos and sin:

Then we use the inverse sin button on our calculator to find the reference angle. (Be sure your calculator is set for radian angles. If you don't know how to set the mode then find the angle in degrees and then multiply your answer by to convert it to radians.)

So our reference angle is 0.46364761 radians. With a cos that is negative and a sin that is positive, must terminate in the 2nd quadrant. To find an angle in the 2nd quadrant, you subtract the reference angle from :

So