(a-bi)(3+5i)=0

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Solution for (a-bi)(3+5i)=0 equation:


Simplifying
(a + -1bi)(3 + 5i) = 0

Multiply (a + -1bi) * (3 + 5i)
(a(3 + 5i) + -1bi * (3 + 5i)) = 0
((3 * a + 5i * a) + -1bi * (3 + 5i)) = 0
((3a + 5ai) + -1bi * (3 + 5i)) = 0
(3a + 5ai + (3 * -1bi + 5i * -1bi)) = 0
(3a + 5ai + (-3bi + -5bi2)) = 0
(3a + 5ai + -3bi + -5bi2) = 0

Solving
3a + 5ai + -3bi + -5bi2 = 0

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 = 0 + 3bi

Combine like terms: -3bi + 3bi = 0
3a + 5ai + 0 + -5bi2 = 0 + 3bi
3a + 5ai + -5bi2 = 0 + 3bi
Remove the zero:
3a + 5ai + -5bi2 = 3bi

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

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

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

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

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

The solution to this equation could not be determined.

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