(-8+2i)(3+i)=

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Solution for (-8+2i)(3+i)= equation:


Simplifying
(-8 + 2i)(3 + i) = 0

Multiply (-8 + 2i) * (3 + i)
(-8(3 + i) + 2i * (3 + i)) = 0
((3 * -8 + i * -8) + 2i * (3 + i)) = 0
((-24 + -8i) + 2i * (3 + i)) = 0
(-24 + -8i + (3 * 2i + i * 2i)) = 0
(-24 + -8i + (6i + 2i2)) = 0

Combine like terms: -8i + 6i = -2i
(-24 + -2i + 2i2) = 0

Solving
-24 + -2i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1i + i2) = 0

Factor a trinomial.
2((-3 + -1i)(4 + -1i)) = 0

Ignore the factor 2.

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 '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4

Solution

i = {-3, 4}

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