(-4-8i)(3+i)=

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Solution for (-4-8i)(3+i)= equation:


Simplifying
(-4 + -8i)(3 + i) = 0

Multiply (-4 + -8i) * (3 + i)
(-4(3 + i) + -8i * (3 + i)) = 0
((3 * -4 + i * -4) + -8i * (3 + i)) = 0
((-12 + -4i) + -8i * (3 + i)) = 0
(-12 + -4i + (3 * -8i + i * -8i)) = 0
(-12 + -4i + (-24i + -8i2)) = 0

Combine like terms: -4i + -24i = -28i
(-12 + -28i + -8i2) = 0

Solving
-12 + -28i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(3 + 7i + 2i2) = 0

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

Ignore the factor -4.

Subproblem 1

Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3

Subproblem 2

Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5

Solution

i = {-3, -0.5}

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