(3-2i)(-4+i)=0

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Solution for (3-2i)(-4+i)=0 equation:


Simplifying
(3 + -2i)(-4 + i) = 0

Multiply (3 + -2i) * (-4 + i)
(3(-4 + i) + -2i * (-4 + i)) = 0
((-4 * 3 + i * 3) + -2i * (-4 + i)) = 0
((-12 + 3i) + -2i * (-4 + i)) = 0
(-12 + 3i + (-4 * -2i + i * -2i)) = 0
(-12 + 3i + (8i + -2i2)) = 0

Combine like terms: 3i + 8i = 11i
(-12 + 11i + -2i2) = 0

Solving
-12 + 11i + -2i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-4 + i)(3 + -2i) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5

Solution

i = {4, 1.5}

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