(3+4i)(3-4i)=0

Solution for (3+4i)(3-4i)=0 equation:

Simplifying
(3 + 4i)(3 + -4i) = 0

Multiply (3 + 4i) * (3 + -4i)
(3(3 + -4i) + 4i * (3 + -4i)) = 0
((3 * 3 + -4i * 3) + 4i * (3 + -4i)) = 0
((9 + -12i) + 4i * (3 + -4i)) = 0
(9 + -12i + (3 * 4i + -4i * 4i)) = 0
(9 + -12i + (12i + -16i2)) = 0

Combine like terms: -12i + 12i = 0
(9 + 0 + -16i2) = 0
(9 + -16i2) = 0

Solving
9 + -16i2 = 0

Solving for variable 'i'.

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

Add '-9' to each side of the equation.
9 + -9 + -16i2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -16i2 = 0 + -9
-16i2 = 0 + -9

Combine like terms: 0 + -9 = -9
-16i2 = -9

Divide each side by '-16'.
i2 = 0.5625

Simplifying
i2 = 0.5625

Take the square root of each side:
i = {-0.75, 0.75}