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

The answer is 49 because it is...

Find two complex numbers that have a sum of i10

theblondeone2

08.01.2022

-2+5i and 2+5i

Step-by-step 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 $-2+5i\textrm{ and }2+5i$ .

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