(5-i)+(2+4i)-(4+2i)=

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Solution for (5-i)+(2+4i)-(4+2i)= equation:


Simplifying
(5 + -1i) + (2 + 4i) + -1(4 + 2i) = 0

Remove parenthesis around (5 + -1i)
5 + -1i + (2 + 4i) + -1(4 + 2i) = 0

Remove parenthesis around (2 + 4i)
5 + -1i + 2 + 4i + -1(4 + 2i) = 0
5 + -1i + 2 + 4i + (4 * -1 + 2i * -1) = 0
5 + -1i + 2 + 4i + (-4 + -2i) = 0

Reorder the terms:
5 + 2 + -4 + -1i + 4i + -2i = 0

Combine like terms: 5 + 2 = 7
7 + -4 + -1i + 4i + -2i = 0

Combine like terms: 7 + -4 = 3
3 + -1i + 4i + -2i = 0

Combine like terms: -1i + 4i = 3i
3 + 3i + -2i = 0

Combine like terms: 3i + -2i = 1i
3 + 1i = 0

Solving
3 + 1i = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + -3 + 1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 1i = 0 + -3
1i = 0 + -3

Combine like terms: 0 + -3 = -3
1i = -3

Divide each side by '1'.
i = -3

Simplifying
i = -3

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