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

Question

asked Dec 20, 2020 205k views

1 Answer

Tazz · Answer 1 · 2020-12-24T08:57:01+0000

Explanation:

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

Given, sum is
10i , difference is
and product is
.

(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
$-2+5i\textrm{ and }2+5i$ .