Complex numbers?

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?

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.

Reply 2

TenOfThem

18

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

(edited 9 years ago)

Reply 3

bubblegum21

OP

3

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?

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?