(8-4i)(-3+9i)=0

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Solution for (8-4i)(-3+9i)=0 equation:


Simplifying
(8 + -4i)(-3 + 9i) = 0

Multiply (8 + -4i) * (-3 + 9i)
(8(-3 + 9i) + -4i * (-3 + 9i)) = 0
((-3 * 8 + 9i * 8) + -4i * (-3 + 9i)) = 0
((-24 + 72i) + -4i * (-3 + 9i)) = 0
(-24 + 72i + (-3 * -4i + 9i * -4i)) = 0
(-24 + 72i + (12i + -36i2)) = 0

Combine like terms: 72i + 12i = 84i
(-24 + 84i + -36i2) = 0

Solving
-24 + 84i + -36i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + 7i + -3i2) = 0

Factor a trinomial.
12((-2 + i)(1 + -3i)) = 0

Ignore the factor 12.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333

Solution

i = {2, 0.3333333333}

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