(-2+3i)*(8-i)=0

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Solution for (-2+3i)*(8-i)=0 equation: 


Simplifying
(-2 + 3i)(8 + -1i) = 0

Multiply (-2 + 3i) * (8 + -1i)
(-2(8 + -1i) + 3i * (8 + -1i)) = 0
((8 * -2 + -1i * -2) + 3i * (8 + -1i)) = 0
((-16 + 2i) + 3i * (8 + -1i)) = 0
(-16 + 2i + (8 * 3i + -1i * 3i)) = 0
(-16 + 2i + (24i + -3i2)) = 0

Combine like terms: 2i + 24i = 26i
(-16 + 26i + -3i2) = 0

Solving
-16 + 26i + -3i2 = 0

Solving for variable 'i'.

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


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

Simplifying
-8 + i = 0

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

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

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

Simplifying
i = 8

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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Solution
i = {8, 0.6666666667}

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