(a+bi)(6-7i)=53+9i

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Solution for (a+bi)(6-7i)=53+9i equation: 


Simplifying
(a + bi)(6 + -7i) = 53 + 9i

Multiply (a + bi) * (6 + -7i)
(a(6 + -7i) + bi(6 + -7i)) = 53 + 9i
((6 * a + -7i * a) + bi(6 + -7i)) = 53 + 9i
((6a + -7ai) + bi(6 + -7i)) = 53 + 9i
(6a + -7ai + (6 * bi + -7i * bi)) = 53 + 9i
(6a + -7ai + (6bi + -7bi2)) = 53 + 9i
(6a + -7ai + 6bi + -7bi2) = 53 + 9i

Solving
6a + -7ai + 6bi + -7bi2 = 53 + 9i

Solving for variable 'a'.

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

Add '-6bi' to each side of the equation.
6a + -7ai + 6bi + -6bi + -7bi2 = 53 + -6bi + 9i

Combine like terms: 6bi + -6bi = 0
6a + -7ai + 0 + -7bi2 = 53 + -6bi + 9i
6a + -7ai + -7bi2 = 53 + -6bi + 9i

Add '7bi2' to each side of the equation.
6a + -7ai + -7bi2 + 7bi2 = 53 + -6bi + 7bi2 + 9i

Combine like terms: -7bi2 + 7bi2 = 0
6a + -7ai + 0 = 53 + -6bi + 7bi2 + 9i
6a + -7ai = 53 + -6bi + 7bi2 + 9i

Reorder the terms:
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 53 + -6bi + 7bi2 + 9i + -53 + 6bi + -7bi2 + -9i

Reorder the terms:
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 53 + -53 + -6bi + 6bi + 7bi2 + -7bi2 + 9i + -9i

Combine like terms: 53 + -53 = 0
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 0 + -6bi + 6bi + 7bi2 + -7bi2 + 9i + -9i
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = -6bi + 6bi + 7bi2 + -7bi2 + 9i + -9i

Combine like terms: -6bi + 6bi = 0
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 0 + 7bi2 + -7bi2 + 9i + -9i
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 7bi2 + -7bi2 + 9i + -9i

Combine like terms: 7bi2 + -7bi2 = 0
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 0 + 9i + -9i
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 9i + -9i

Combine like terms: 9i + -9i = 0
-53 + 6a + -7ai + 6bi + -7bi2 + -9i = 0

The solution to this equation could not be determined.

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