I found these two questions in a textbook and they are driving me nuts. (Thinking)

How can you derive from that ?

Similarly, how can you with the help of show that

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- Dec 26th 2009, 03:00 AMMondreusComplex arctan
I found these two questions in a textbook and they are driving me nuts. (Thinking)

How can you derive from that ?

Similarly, how can you with the help of show that - Dec 26th 2009, 03:47 AMHallsofIvy
1+ i can be written, in polar form, as where (and, of course, ). 2+ i can be written as where . 3+ i can be written as where .

By DeMoivre's formula, their product is .

The fact that the product is 10 i tells you that and or that .

Quote:

Similarly, how can you with the help of show that

- Dec 26th 2009, 04:21 AMMondreus
What about the part in the last problem?

- Dec 26th 2009, 06:08 AMHallsofIvy
Consider which quadrant you are in.

- Dec 26th 2009, 03:25 PM11rdc11

Wow this problem is confusing. It took me a little bit to figure it out.

HallsofIvy you have a typo when you said

it should be

Thanks for working it out though. It really did help me figure out my mistake.

I kept working out

Since the original problem was in the second quad. Didn't notice the tan had been changed to positive value changing the problem. - Dec 26th 2009, 04:59 PMHallsofIvy
Yes, thanks for the correction.

Quote:

Thanks for working it out though. It really did help me figure out my mistake.

I kept working out

Since the original problem was in the second quad. Didn't notice the tan had been changed to positive value changing the problem.