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

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


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

Multiply (4 + 3i) * (2 + -2i)
(4(2 + -2i) + 3i * (2 + -2i)) = 0
((2 * 4 + -2i * 4) + 3i * (2 + -2i)) = 0
((8 + -8i) + 3i * (2 + -2i)) = 0
(8 + -8i + (2 * 3i + -2i * 3i)) = 0
(8 + -8i + (6i + -6i2)) = 0

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

Solving
8 + -2i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -1i + -3i2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 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 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333

Solution

i = {1, -1.333333333}

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