(5-4i)(10+8i)=0

Solution for (5-4i)(10+8i)=0 equation:

Simplifying
(5 + -4i)(10 + 8i) = 0

Multiply (5 + -4i) * (10 + 8i)
(5(10 + 8i) + -4i * (10 + 8i)) = 0
((10 * 5 + 8i * 5) + -4i * (10 + 8i)) = 0
((50 + 40i) + -4i * (10 + 8i)) = 0
(50 + 40i + (10 * -4i + 8i * -4i)) = 0
(50 + 40i + (-40i + -32i2)) = 0

Combine like terms: 40i + -40i = 0
(50 + 0 + -32i2) = 0
(50 + -32i2) = 0

Solving
50 + -32i2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-50' to each side of the equation.
50 + -50 + -32i2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -32i2 = 0 + -50
-32i2 = 0 + -50

Combine like terms: 0 + -50 = -50
-32i2 = -50

Divide each side by '-32'.
i2 = 1.5625

Simplifying
i2 = 1.5625

Take the square root of each side:
i = {-1.25, 1.25}