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# Solve z^5 = 1 + j. Can someone help walk me through this? watch

1. z^5 = 1 + j. Just a guide on how to approach and solve this. Thanks. Please walkthrough it in baby steps i am completely new to this.
2. (Original post by MatthewTG)
z^5 = 1 + j. Just a guide on how to approach and solve this. Thanks.
What have you tried?
3. (Original post by MatthewTG)
z^5 = 1 + j. Just a guide on how to approach and solve this. Thanks.
Express both sides as complex-exponentials
4. (Original post by Mr M)
What have you tried?
I think the de moivre theorum is used but im not sure
5. if z = re

then z5 = r5ei5Θ

and 1 + i = √2e iπ/4

so r5ei5Θ = √2e iπ/4

now you should be able to find values for r and
Θ
6. (Original post by MatthewTG)
I think the de moivre theorum is used but im not sure
What's the modulus and argument of 1 + j ?
7. (Original post by MatthewTG)
I think the de moivre theorum is used but im not sure
De Moivre's theorem states that which doesn't really help with it. It might, though it seems a bit long winded.

Anyhow, the best way to approach this is to express your complex number in the form and then take the 5th root of both sides - keep in mind that you should have 5 solutions as you consider the period of the solutions.
8. (Original post by Mr M)
x
Good evening, Mr M. Do you know if this is a question I could get in FP1 (OCR MEI)?
9. (Original post by karmacrunch)
Good evening, Mr M. Do you know if this is a question I could get in FP1 (OCR MEI)?
No you couldn't. It's FP2.
10. (Original post by Mr M)
No you couldn't. It's FP2.
Thank you!
11. (Original post by the bear)
if z = re

then z5 = r5ei5Θ

and 1 + i = √2e iπ/4

so r5ei5Θ = √2e iπ/4

now you should be able to find values for r and
Θ
You also need to take general form of the argument into account - the argument can be altered by any multiple of without changing the complex number. So we want:

for

else we won't get all of the solutions - there are 5.
12. (Original post by atsruser)
You also need to take general form of the argument into account - the argument can be altered by any multiple of without changing the complex number. So we want:

for

else we won't get all of the solutions - there are 5.
i did not want to make it too easy.
13. (Original post by the bear)
i did not want to make it too easy.
I see that the bear is a harsh and demanding taskmaster.
14. (Original post by atsruser)
I see that the bear is a harsh and demanding taskmaster.

also bear™ is not a huge fan of j

15. (Original post by the bear)

also bear™ is not a huge fan of j

The standard desensitisation therapy for that ailment is to force yourself to read a large number of electronic and electrical engineering texts - in severe cases, the treatment also involves a straitjacket, eyelid separators, and a CD of Beethoven's Ninth symphony.
16. (Original post by atsruser)
The standard desensitisation therapy for that ailment is to force yourself to read a large number of electronic and electrical engineering texts - in severe cases, the treatment also involves a straitjacket, eyelid separators, and a CD of Beethoven's Ninth symphony.
that is just weird... like a mechanical mandarin or something ?

j =
17. (Original post by the bear)
that is just weird... like a mechanical mandarin or something ?
Or maybe like an automated tangerine?

Anyway, it's late - time for a little spatchka.
18. (Original post by atsruser)
Or maybe like an automated tangerine?

Anyway, it's late - time for a little spatchka.
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