Products & Quotients of Complex Numbers in Polar Form

greatwhiteshark

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May 8, 2005
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d = degrees

If z = 3(cos20d + i sin20d) and w = 5(cos100d + i sin100d), find the following: zw and z/w.

I understand how to find z times w or zw but get lost after a certain step in terms of dividing z by w or z/w.

z/w = 3(cos20d + isin20d)/5(cos100d + i sin100d)

z/w = 3/5[cos(20d - 100d) + i sin(20d -100d)]

z/w = 3/5[cos(-80) + 1 sin(-80)]

After this step, the book's answer is

z/w = 3/5(cos280d + i sin280d)

Then it states: "Argument must lie between 0d and 360d."

Two question:

1) Where did 280 degrees come from in the final step?

2) What does the author mean by "Argument must lie between 0d and 360d"?
 
2) What does the author mean by "Argument must lie between 0d and 360d"?

The angle has to be between 0 and 360 degrees. You had -80, which is not between 0 and 360.

1) Where did 280 degrees come from in the final step?

To change -80 degrees to an angle between 0 and 360 degrees, go around the circle once counter-clockwise. That is, add 360 degrees to it.
 
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