(-7+4i)(8-7i)=0

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Solution for (-7+4i)(8-7i)=0 equation: 


Simplifying
(-7 + 4i)(8 + -7i) = 0

Multiply (-7 + 4i) * (8 + -7i)
(-7(8 + -7i) + 4i * (8 + -7i)) = 0
((8 * -7 + -7i * -7) + 4i * (8 + -7i)) = 0
((-56 + 49i) + 4i * (8 + -7i)) = 0
(-56 + 49i + (8 * 4i + -7i * 4i)) = 0
(-56 + 49i + (32i + -28i2)) = 0

Combine like terms: 49i + 32i = 81i
(-56 + 81i + -28i2) = 0

Solving
-56 + 81i + -28i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-7 + 4i)(8 + -7i) = 0


Subproblem 1
Set the factor '(-7 + 4i)' equal to zero and attempt to solve:

Simplifying
-7 + 4i = 0

Solving
-7 + 4i = 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 + 4i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4i = 0 + 7
4i = 0 + 7

Combine like terms: 0 + 7 = 7
4i = 7

Divide each side by '4'.
i = 1.75

Simplifying
i = 1.75

Subproblem 2
Set the factor '(8 + -7i)' equal to zero and attempt to solve:

Simplifying
8 + -7i = 0

Solving
8 + -7i = 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 + -7i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7i = 0 + -8
-7i = 0 + -8

Combine like terms: 0 + -8 = -8
-7i = -8

Divide each side by '-7'.
i = 1.142857143

Simplifying
i = 1.142857143
Solution
i = {1.75, 1.142857143}

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