(3-5i)(a+bi)=2-i

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Solution for (3-5i)(a+bi)=2-i equation: 


Simplifying
(3 + -5i)(a + bi) = 2 + -1i

Multiply (3 + -5i) * (a + bi)
(3(a + bi) + -5i * (a + bi)) = 2 + -1i
((a * 3 + bi * 3) + -5i * (a + bi)) = 2 + -1i
((3a + 3bi) + -5i * (a + bi)) = 2 + -1i
(3a + 3bi + (a * -5i + bi * -5i)) = 2 + -1i
(3a + 3bi + (-5ai + -5bi2)) = 2 + -1i

Reorder the terms:
(3a + -5ai + 3bi + -5bi2) = 2 + -1i
(3a + -5ai + 3bi + -5bi2) = 2 + -1i

Solving
3a + -5ai + 3bi + -5bi2 = 2 + -1i

Solving for variable 'a'.

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

Add '-3bi' to each side of the equation.
3a + -5ai + 3bi + -3bi + -5bi2 = 2 + -3bi + -1i

Combine like terms: 3bi + -3bi = 0
3a + -5ai + 0 + -5bi2 = 2 + -3bi + -1i
3a + -5ai + -5bi2 = 2 + -3bi + -1i

Add '5bi2' to each side of the equation.
3a + -5ai + -5bi2 + 5bi2 = 2 + -3bi + 5bi2 + -1i

Combine like terms: -5bi2 + 5bi2 = 0
3a + -5ai + 0 = 2 + -3bi + 5bi2 + -1i
3a + -5ai = 2 + -3bi + 5bi2 + -1i

Reorder the terms:
-2 + 3a + -5ai + 3bi + -5bi2 + i = 2 + -3bi + 5bi2 + -1i + -2 + 3bi + -5bi2 + i

Reorder the terms:
-2 + 3a + -5ai + 3bi + -5bi2 + i = 2 + -2 + -3bi + 3bi + 5bi2 + -5bi2 + -1i + i

Combine like terms: 2 + -2 = 0
-2 + 3a + -5ai + 3bi + -5bi2 + i = 0 + -3bi + 3bi + 5bi2 + -5bi2 + -1i + i
-2 + 3a + -5ai + 3bi + -5bi2 + i = -3bi + 3bi + 5bi2 + -5bi2 + -1i + i

Combine like terms: -3bi + 3bi = 0
-2 + 3a + -5ai + 3bi + -5bi2 + i = 0 + 5bi2 + -5bi2 + -1i + i
-2 + 3a + -5ai + 3bi + -5bi2 + i = 5bi2 + -5bi2 + -1i + i

Combine like terms: 5bi2 + -5bi2 = 0
-2 + 3a + -5ai + 3bi + -5bi2 + i = 0 + -1i + i
-2 + 3a + -5ai + 3bi + -5bi2 + i = -1i + i

Combine like terms: -1i + i = 0
-2 + 3a + -5ai + 3bi + -5bi2 + i = 0

The solution to this equation could not be determined.

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