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

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

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

Multiply (5 + 8i) * (5 + -8i)
(5(5 + -8i) + 8i * (5 + -8i)) = 0
((5 * 5 + -8i * 5) + 8i * (5 + -8i)) = 0
((25 + -40i) + 8i * (5 + -8i)) = 0
(25 + -40i + (5 * 8i + -8i * 8i)) = 0
(25 + -40i + (40i + -64i2)) = 0

Combine like terms: -40i + 40i = 0
(25 + 0 + -64i2) = 0
(25 + -64i2) = 0

Solving
25 + -64i2 = 0

Solving for variable 'i'.

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

Add '-25' to each side of the equation.
25 + -25 + -64i2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -64i2 = 0 + -25
-64i2 = 0 + -25

Combine like terms: 0 + -25 = -25
-64i2 = -25

Divide each side by '-64'.
i2 = 0.390625

Simplifying
i2 = 0.390625

Take the square root of each side:
i = {-0.625, 0.625}