a+5+(b-2)i=10+6i

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Solution for a+5+(b-2)i=10+6i equation:


Simplifying
a + 5 + (b + -2) * i = 10 + 6i

Reorder the terms:
a + 5 + (-2 + b) * i = 10 + 6i

Reorder the terms for easier multiplication:
a + 5 + i(-2 + b) = 10 + 6i
a + 5 + (-2 * i + b * i) = 10 + 6i

Reorder the terms:
a + 5 + (bi + -2i) = 10 + 6i
a + 5 + (bi + -2i) = 10 + 6i

Reorder the terms:
5 + a + bi + -2i = 10 + 6i

Solving
5 + a + bi + -2i = 10 + 6i

Solving for variable 'a'.

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

Add '-5' to each side of the equation.
5 + a + bi + -5 + -2i = 10 + -5 + 6i

Reorder the terms:
5 + -5 + a + bi + -2i = 10 + -5 + 6i

Combine like terms: 5 + -5 = 0
0 + a + bi + -2i = 10 + -5 + 6i
a + bi + -2i = 10 + -5 + 6i

Combine like terms: 10 + -5 = 5
a + bi + -2i = 5 + 6i

Add '-1bi' to each side of the equation.
a + bi + -1bi + -2i = 5 + -1bi + 6i

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

Add '2i' to each side of the equation.
a + -2i + 2i = 5 + -1bi + 6i + 2i

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

Combine like terms: 6i + 2i = 8i
a = 5 + -1bi + 8i

Simplifying
a = 5 + -1bi + 8i

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