(-5+4i)(3+i)=0

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Solution for (-5+4i)(3+i)=0 equation:


Simplifying
(-5 + 4i)(3 + i) = 0

Multiply (-5 + 4i) * (3 + i)
(-5(3 + i) + 4i * (3 + i)) = 0
((3 * -5 + i * -5) + 4i * (3 + i)) = 0
((-15 + -5i) + 4i * (3 + i)) = 0
(-15 + -5i + (3 * 4i + i * 4i)) = 0
(-15 + -5i + (12i + 4i2)) = 0

Combine like terms: -5i + 12i = 7i
(-15 + 7i + 4i2) = 0

Solving
-15 + 7i + 4i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3 + -1i)(5 + -4i) = 0

Subproblem 1

Set the factor '(-3 + -1i)' equal to zero and attempt to solve: Simplifying -3 + -1i = 0 Solving -3 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3

Subproblem 2

Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25

Solution

i = {-3, 1.25}

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