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

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

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

Multiply (5 + 4i) * (5 + -4i)
(5(5 + -4i) + 4i * (5 + -4i)) = 0
((5 * 5 + -4i * 5) + 4i * (5 + -4i)) = 0
((25 + -20i) + 4i * (5 + -4i)) = 0
(25 + -20i + (5 * 4i + -4i * 4i)) = 0
(25 + -20i + (20i + -16i2)) = 0

Combine like terms: -20i + 20i = 0
(25 + 0 + -16i2) = 0
(25 + -16i2) = 0

Solving
25 + -16i2 = 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 + -16i2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -16i2 = 0 + -25
-16i2 = 0 + -25

Combine like terms: 0 + -25 = -25
-16i2 = -25

Divide each side by '-16'.
i2 = 1.5625

Simplifying
i2 = 1.5625

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