(8-9i)(2+6i)=

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Solution for (8-9i)(2+6i)= equation: 


Simplifying
(8 + -9i)(2 + 6i) = 0

Multiply (8 + -9i) * (2 + 6i)
(8(2 + 6i) + -9i * (2 + 6i)) = 0
((2 * 8 + 6i * 8) + -9i * (2 + 6i)) = 0
((16 + 48i) + -9i * (2 + 6i)) = 0
(16 + 48i + (2 * -9i + 6i * -9i)) = 0
(16 + 48i + (-18i + -54i2)) = 0

Combine like terms: 48i + -18i = 30i
(16 + 30i + -54i2) = 0

Solving
16 + 30i + -54i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 15i + -27i2) = 0

Factor a trinomial.
2((8 + -9i)(1 + 3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -9i)' equal to zero and attempt to solve:

Simplifying
8 + -9i = 0

Solving
8 + -9i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -9i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9i = 0 + -8
-9i = 0 + -8

Combine like terms: 0 + -8 = -8
-9i = -8

Divide each side by '-9'.
i = 0.8888888889

Simplifying
i = 0.8888888889

Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve:

Simplifying
1 + 3i = 0

Solving
1 + 3i = 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 + 3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3i = 0 + -1
3i = 0 + -1

Combine like terms: 0 + -1 = -1
3i = -1

Divide each side by '3'.
i = -0.3333333333

Simplifying
i = -0.3333333333
Solution
i = {0.8888888889, -0.3333333333}

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