(a-2i)=(3+i)(b-i)

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Solution for (a-2i)=(3+i)(b-i) equation: 


Simplifying
(a + -2i) = (3 + i)(b + -1i)

Remove parenthesis around (a + -2i)
a + -2i = (3 + i)(b + -1i)

Multiply (3 + i) * (b + -1i)
a + -2i = (3(b + -1i) + i(b + -1i))
a + -2i = ((b * 3 + -1i * 3) + i(b + -1i))
a + -2i = ((3b + -3i) + i(b + -1i))
a + -2i = (3b + -3i + (b * i + -1i * i))
a + -2i = (3b + -3i + (bi + -1i2))

Reorder the terms:
a + -2i = (3b + bi + -3i + -1i2)
a + -2i = (3b + bi + -3i + -1i2)

Solving
a + -2i = 3b + bi + -3i + -1i2

Solving for variable 'a'.

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

Add '2i' to each side of the equation.
a + -2i + 2i = 3b + bi + -3i + 2i + -1i2

Combine like terms: -2i + 2i = 0
a + 0 = 3b + bi + -3i + 2i + -1i2
a = 3b + bi + -3i + 2i + -1i2

Combine like terms: -3i + 2i = -1i
a = 3b + bi + -1i + -1i2

Simplifying
a = 3b + bi + -1i + -1i2

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