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

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


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

Multiply (6 + 4i) * (5 + i)
(6(5 + i) + 4i * (5 + i)) = 0
((5 * 6 + i * 6) + 4i * (5 + i)) = 0
((30 + 6i) + 4i * (5 + i)) = 0
(30 + 6i + (5 * 4i + i * 4i)) = 0
(30 + 6i + (20i + 4i2)) = 0

Combine like terms: 6i + 20i = 26i
(30 + 26i + 4i2) = 0

Solving
30 + 26i + 4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 13i + 2i2) = 0

Factor a trinomial.
2((5 + i)(3 + 2i)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5

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 = {-5, -1.5}

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