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# Roots of complex numbers watch

1. The question is find the 5th root of 1+2i. I have found r to be sqrt(5) but finding theta is causing me trouble because I'm getting a decimal and I'm not sure how to carry on with a decimal
2. 1+2i can be written as √5*ei*arctan2

so if a 5th root of 1 + 2i is w ....

w5 = √5*ei*arctan2

...
3. (Original post by Lunu)
The question is find the 5th root of 1+2i. I have found r to be sqrt(5) but finding theta is causing me trouble because I'm getting a decimal and I'm not sure how to carry on with a decimal
or you just leave it as a decimal and continue normally?

i.e: .

But I'd leave it as to be honest. Then it's just:

4. Express a+bi in terms of r(cos(theta + 2kpi) +isin(theta + 2kpi)). To find the fifth root, every term is to the power of 1/5 (in the case of arguments they're divided by 5) and then sub in different whole values for k to find the argument. Remember the argument has to be within minus pi and positive pi.
5. (Original post by the bear)
1+2i can be written as √5*ei*arctan2

so if a 5th root of 1 + 2i is w ....

w5 = √5*ei*arctan2

...
Do you prefer doing these questions with complex numbers in exponential form?
6. (Original post by B_9710)
Do you prefer doing these questions with complex numbers in exponential form?
i find it convenient... you can always do sin and cos later...
7. Thanks everyone!

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