(1+2i)(1-2i)=0

Solution for (1+2i)(1-2i)=0 equation:

Simplifying
(1 + 2i)(1 + -2i) = 0

Multiply (1 + 2i) * (1 + -2i)
(1(1 + -2i) + 2i * (1 + -2i)) = 0
((1 * 1 + -2i * 1) + 2i * (1 + -2i)) = 0
((1 + -2i) + 2i * (1 + -2i)) = 0
(1 + -2i + (1 * 2i + -2i * 2i)) = 0
(1 + -2i + (2i + -4i2)) = 0

Combine like terms: -2i + 2i = 0
(1 + 0 + -4i2) = 0
(1 + -4i2) = 0

Solving
1 + -4i2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -1 + -4i2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4i2 = 0 + -1
-4i2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4i2 = -1

Divide each side by '-4'.
i2 = 0.25

Simplifying
i2 = 0.25

Take the square root of each side:
i = {-0.5, 0.5}