(3-7i)(8+3i)=0

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Solution for (3-7i)(8+3i)=0 equation: 


Simplifying
(3 + -7i)(8 + 3i) = 0

Multiply (3 + -7i) * (8 + 3i)
(3(8 + 3i) + -7i * (8 + 3i)) = 0
((8 * 3 + 3i * 3) + -7i * (8 + 3i)) = 0
((24 + 9i) + -7i * (8 + 3i)) = 0
(24 + 9i + (8 * -7i + 3i * -7i)) = 0
(24 + 9i + (-56i + -21i2)) = 0

Combine like terms: 9i + -56i = -47i
(24 + -47i + -21i2) = 0

Solving
24 + -47i + -21i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -7i)(8 + 3i) = 0


Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve:

Simplifying
3 + -7i = 0

Solving
3 + -7i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7i = 0 + -3
-7i = 0 + -3

Combine like terms: 0 + -3 = -3
-7i = -3

Divide each side by '-7'.
i = 0.4285714286

Simplifying
i = 0.4285714286

Subproblem 2
Set the factor '(8 + 3i)' equal to zero and attempt to solve:

Simplifying
8 + 3i = 0

Solving
8 + 3i = 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 + 3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3i = 0 + -8
3i = 0 + -8

Combine like terms: 0 + -8 = -8
3i = -8

Divide each side by '3'.
i = -2.666666667

Simplifying
i = -2.666666667
Solution
i = {0.4285714286, -2.666666667}

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