Question

Find two complex numbers that have a sum of i10 a different of -4and a product of -29​

Answer 1

-2+5i and 2+5i

Explanation:

Let the complex numbers be
`a+ib\textrm{ and }c+id`.

Given, sum is
`10i`, difference is
`-4` and product is
`-29`.

`(a+c)+i(b+d)=10i` ⇒
`a+c=0,b+d=10`

`(a-c)+i(b-d)=-4` ⇒
`a-c=-4,b-d=0`

`a=-2,c=2,b=5,d=5`

`(a+ib)(c+id)=(-2+5i)(2+5i)=-4-25=-29`

Hence, all three equations are consistent yielding the complex numbers
`-2+5i\textrm{ and }2+5i`.