(7-8i)*(1+i)=0

Solution for (7-8i)*(1+i)=0 equation:

(7-8i)(1+i)=0

We add all the numbers together, and all the variables

(-8i+7)(i+1)=0

We multiply parentheses ..

(-8i^2-8i+7i+7)=0

We get rid of parentheses

-8i^2-8i+7i+7=0

We add all the numbers together, and all the variables

-8i^2-1i+7=0

a = -8; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-8)·7
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*-8}=\frac{-14}{-16}
=7/8
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*-8}=\frac{16}{-16}
=-1
$