(-7+9i)(2-10i)=

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Solution for (-7+9i)(2-10i)= equation: 


Simplifying
(-7 + 9i)(2 + -10i) = 0

Multiply (-7 + 9i) * (2 + -10i)
(-7(2 + -10i) + 9i * (2 + -10i)) = 0
((2 * -7 + -10i * -7) + 9i * (2 + -10i)) = 0
((-14 + 70i) + 9i * (2 + -10i)) = 0
(-14 + 70i + (2 * 9i + -10i * 9i)) = 0
(-14 + 70i + (18i + -90i2)) = 0

Combine like terms: 70i + 18i = 88i
(-14 + 88i + -90i2) = 0

Solving
-14 + 88i + -90i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 44i + -45i2) = 0

Factor a trinomial.
2((-7 + 9i)(1 + -5i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 9i)' equal to zero and attempt to solve:

Simplifying
-7 + 9i = 0

Solving
-7 + 9i = 0

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

Add '7' to each side of the equation.
-7 + 7 + 9i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 9i = 0 + 7
9i = 0 + 7

Combine like terms: 0 + 7 = 7
9i = 7

Divide each side by '9'.
i = 0.7777777778

Simplifying
i = 0.7777777778

Subproblem 2
Set the factor '(1 + -5i)' equal to zero and attempt to solve:

Simplifying
1 + -5i = 0

Solving
1 + -5i = 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 + -5i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5i = 0 + -1
-5i = 0 + -1

Combine like terms: 0 + -1 = -1
-5i = -1

Divide each side by '-5'.
i = 0.2

Simplifying
i = 0.2
Solution
i = {0.7777777778, 0.2}

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