(1+7i)(1-7i)=0

Solution for (1+7i)(1-7i)=0 equation:

Simplifying
(1 + 7i)(1 + -7i) = 0

Multiply (1 + 7i) * (1 + -7i)
(1(1 + -7i) + 7i * (1 + -7i)) = 0
((1 * 1 + -7i * 1) + 7i * (1 + -7i)) = 0
((1 + -7i) + 7i * (1 + -7i)) = 0
(1 + -7i + (1 * 7i + -7i * 7i)) = 0
(1 + -7i + (7i + -49i2)) = 0

Combine like terms: -7i + 7i = 0
(1 + 0 + -49i2) = 0
(1 + -49i2) = 0

Solving
1 + -49i2 = 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 + -49i2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -49i2 = 0 + -1
-49i2 = 0 + -1

Combine like terms: 0 + -1 = -1
-49i2 = -1

Divide each side by '-49'.
i2 = 0.02040816327

Simplifying
i2 = 0.02040816327

Take the square root of each side:
i = {-0.142857143, 0.142857143}