Need help with complex numbers question.Watch

Thread starter 4 weeks ago
#1
Find in exponential form (2+2i)^(4/3). There’s meant to be more than one answer. Please show working out so I understand it.
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4 weeks ago
#2
(Original post by Adil2400)
Find in exponential form (2+2i)^(4/3). There’s meant to be more than one answer. Please show working out so I understand it.
Convert 2+2i into exponential form first.
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4 weeks ago
#3
First thoughts: Let z=a+bi. Let z^3 = (2+2i)^4. To work this out, you can use the modulus and argument of each of them, and find out which arguments equate.
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Thread starter 4 weeks ago
#4
(Original post by RDKGames)
Convert 2+2i into exponential form first.
I can do that but how many answers are there supposed to be? If we were working out (2+2i)^(1/3), there would be 3 answers. How many answers are there for (2+2i)^(4/3)?
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4 weeks ago
#5
(Original post by Adil2400)
I can do that but how many answers are there supposed to be? If we were working out (2+2i)^(1/3), there would be 3 answers. How many answers are there for (2+2i)^(4/3)?
Still three, because of the cube root.
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Thread starter 4 weeks ago
#6
(Original post by RDKGames)
Still three, because of the cube root.
How do you know there’s not 4 because of the power of 4?
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4 weeks ago
#7
(Original post by Adil2400)
How do you know there’s not 4 because of the power of 4?
Because you're not taking a fourth root...

At the end of the day nth root means we are solving some equation and by Fundamental Theorem of Algebra we know this has n roots.
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Thread starter 4 weeks ago
#8
(Original post by RDKGames)
Because you're not taking a fourth root...

At the end of the day nth root means we are solving some equation and by Fundamental Theorem of Algebra we know this has n roots.
ok thanks. If you can, please attempt the question and tell me what you get. I want to see if I get the same answers.
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4 weeks ago
#9
(Original post by Adil2400)
ok thanks. If you can, please attempt the question and tell me what you get. I want to see if I get the same answers.
Easier if you post your answers here and I just look at them tbh
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