(-2+4i)(-5+6i)=

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Solution for (-2+4i)(-5+6i)= equation:


Simplifying
(-2 + 4i)(-5 + 6i) = 0

Multiply (-2 + 4i) * (-5 + 6i)
(-2(-5 + 6i) + 4i * (-5 + 6i)) = 0
((-5 * -2 + 6i * -2) + 4i * (-5 + 6i)) = 0
((10 + -12i) + 4i * (-5 + 6i)) = 0
(10 + -12i + (-5 * 4i + 6i * 4i)) = 0
(10 + -12i + (-20i + 24i2)) = 0

Combine like terms: -12i + -20i = -32i
(10 + -32i + 24i2) = 0

Solving
10 + -32i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -16i + 12i2) = 0

Factor a trinomial.
2((1 + -2i)(5 + -6i)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333

Solution

i = {0.5, 0.8333333333}

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