(9+3i)-(6+10i)+(1+9i)=0

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Solution for (9+3i)-(6+10i)+(1+9i)=0 equation:


Simplifying
(9 + 3i) + -1(6 + 10i) + (1 + 9i) = 0

Remove parenthesis around (9 + 3i)
9 + 3i + -1(6 + 10i) + (1 + 9i) = 0
9 + 3i + (6 * -1 + 10i * -1) + (1 + 9i) = 0
9 + 3i + (-6 + -10i) + (1 + 9i) = 0

Remove parenthesis around (1 + 9i)
9 + 3i + -6 + -10i + 1 + 9i = 0

Reorder the terms:
9 + -6 + 1 + 3i + -10i + 9i = 0

Combine like terms: 9 + -6 = 3
3 + 1 + 3i + -10i + 9i = 0

Combine like terms: 3 + 1 = 4
4 + 3i + -10i + 9i = 0

Combine like terms: 3i + -10i = -7i
4 + -7i + 9i = 0

Combine like terms: -7i + 9i = 2i
4 + 2i = 0

Solving
4 + 2i = 0

Solving for variable 'i'.

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

Add '-4' to each side of the equation.
4 + -4 + 2i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2i = 0 + -4
2i = 0 + -4

Combine like terms: 0 + -4 = -4
2i = -4

Divide each side by '2'.
i = -2

Simplifying
i = -2

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