a-2i=(1+bi)(2-i)

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Solution for a-2i=(1+bi)(2-i) equation: 


Simplifying
a + -2i = (1 + bi)(2 + -1i)

Multiply (1 + bi) * (2 + -1i)
a + -2i = (1(2 + -1i) + bi(2 + -1i))
a + -2i = ((2 * 1 + -1i * 1) + bi(2 + -1i))
a + -2i = ((2 + -1i) + bi(2 + -1i))
a + -2i = (2 + -1i + (2 * bi + -1i * bi))
a + -2i = (2 + -1i + (2bi + -1bi2))

Reorder the terms:
a + -2i = (2 + 2bi + -1bi2 + -1i)
a + -2i = (2 + 2bi + -1bi2 + -1i)

Solving
a + -2i = 2 + 2bi + -1bi2 + -1i

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 = 2 + 2bi + -1bi2 + -1i + 2i

Combine like terms: -2i + 2i = 0
a + 0 = 2 + 2bi + -1bi2 + -1i + 2i
a = 2 + 2bi + -1bi2 + -1i + 2i

Combine like terms: -1i + 2i = 1i
a = 2 + 2bi + -1bi2 + 1i

Simplifying
a = 2 + 2bi + -1bi2 + 1i

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