(1+5i)+(-6+2i)=0

Solution for (1+5i)+(-6+2i)=0 equation:

Simplifying
(1 + 5i) + (-6 + 2i) = 0

Remove parenthesis around (1 + 5i)
1 + 5i + (-6 + 2i) = 0

Remove parenthesis around (-6 + 2i)
1 + 5i + -6 + 2i = 0

Reorder the terms:
1 + -6 + 5i + 2i = 0

Combine like terms: 1 + -6 = -5
-5 + 5i + 2i = 0

Combine like terms: 5i + 2i = 7i
-5 + 7i = 0

Solving
-5 + 7i = 0

Solving for variable 'i'.

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

Add '5' to each side of the equation.
-5 + 5 + 7i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7i = 0 + 5
7i = 0 + 5

Combine like terms: 0 + 5 = 5
7i = 5

Divide each side by '7'.
i = 0.7142857143

Simplifying
i = 0.7142857143