(3+2i)(2-14i)=

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Solution for (3+2i)(2-14i)= equation:


Simplifying
(3 + 2i)(2 + -14i) = 0

Multiply (3 + 2i) * (2 + -14i)
(3(2 + -14i) + 2i * (2 + -14i)) = 0
((2 * 3 + -14i * 3) + 2i * (2 + -14i)) = 0
((6 + -42i) + 2i * (2 + -14i)) = 0
(6 + -42i + (2 * 2i + -14i * 2i)) = 0
(6 + -42i + (4i + -28i2)) = 0

Combine like terms: -42i + 4i = -38i
(6 + -38i + -28i2) = 0

Solving
6 + -38i + -28i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -19i + -14i2) = 0

Factor a trinomial.
2((1 + -7i)(3 + 2i)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -7i)' equal to zero and attempt to solve: Simplifying 1 + -7i = 0 Solving 1 + -7i = 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 + -7i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7i = 0 + -1 -7i = 0 + -1 Combine like terms: 0 + -1 = -1 -7i = -1 Divide each side by '-7'. i = 0.1428571429 Simplifying i = 0.1428571429

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 = {0.1428571429, -1.5}

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