(8+2i)(5-9i)=

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Solution for (8+2i)(5-9i)= equation: 


Simplifying
(8 + 2i)(5 + -9i) = 0

Multiply (8 + 2i) * (5 + -9i)
(8(5 + -9i) + 2i * (5 + -9i)) = 0
((5 * 8 + -9i * 8) + 2i * (5 + -9i)) = 0
((40 + -72i) + 2i * (5 + -9i)) = 0
(40 + -72i + (5 * 2i + -9i * 2i)) = 0
(40 + -72i + (10i + -18i2)) = 0

Combine like terms: -72i + 10i = -62i
(40 + -62i + -18i2) = 0

Solving
40 + -62i + -18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -31i + -9i2) = 0

Factor a trinomial.
2((5 + -9i)(4 + i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -9i)' equal to zero and attempt to solve:

Simplifying
5 + -9i = 0

Solving
5 + -9i = 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 + -9i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9i = 0 + -5
-9i = 0 + -5

Combine like terms: 0 + -5 = -5
-9i = -5

Divide each side by '-9'.
i = 0.5555555556

Simplifying
i = 0.5555555556

Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve:

Simplifying
4 + i = 0

Solving
4 + i = 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 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
Solution
i = {0.5555555556, -4}

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