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

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

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

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

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

Solving
16 + -25i2 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -16 + -25i2 = 0 + -16

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

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

Divide each side by '-25'.
i2 = 0.64

Simplifying
i2 = 0.64

Take the square root of each side:
i = {-0.8, 0.8}