Complex numbers? Watch

bubblegum21
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I was given this q to answer:Given that (1+i) is a root of x^3 + 2x^2 + wx + u = 0, find the values of w and uI first tried to sub (1+i) in place of x a got down to i^3 + 7i - 2 + w(1+i) + u= 0 I then tried to solve simultaneously to find w and u with no luck. Any suggestions?
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Mr M
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(Original post by bubblegum21)
I was given this q to answer:Given that (1+i) is a root of x^3 + 2x^2 + wx + u = 0, find the values of w and uI first tried to sub (1+i) in place of x a got down to i^3 + 7i - 2 + w(1+i) + u= 0 I then tried to solve simultaneously to find w and u with no luck. Any suggestions?
I expect the question tells you that w and u are real. If so you know a second root as the complex roots occur in conjugate pairs.
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TenOfThem
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(Original post by bubblegum21)
I was given this q to answer:Given that (1+i) is a root of x^3 + 2x^2 + wx + u = 0, find the values of w and uI first tried to sub (1+i) in place of x a got down to i^3 + 7i - 2 + w(1+i) + u= 0 I then tried to solve simultaneously to find w and u with no luck. Any suggestions?
Surely you know that i^3 = -i

So you have

(w+u-2) + (6+w)i = 0

Find w from the imaginary part and then u from the real
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bubblegum21
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(Original post by Mr M)
I expect the question tells you that w and u are real. If so you know a second root as the complex roots occur in conjugate pairs.
I worked with your suggestion and have found values for both w and u. However I subbed both values into the first equation but the answer is not 0. Any ideas where I went wrong?
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Mr M
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(Original post by bubblegum21)
I worked with your suggestion and have found values for both w and u. However I subbed both values into the first equation but the answer is not 0. Any ideas where I went wrong?
No idea. Show your working.
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bubblegum21
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(Original post by Mr M)
No idea. Show your working.
I miscalculated somewhere along the way, I've managed to work it out though. Thanks for the help!
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