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

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