(4-3i)(-5+4i)=0

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Solution for (4-3i)(-5+4i)=0 equation:


Simplifying
(4 + -3i)(-5 + 4i) = 0

Multiply (4 + -3i) * (-5 + 4i)
(4(-5 + 4i) + -3i * (-5 + 4i)) = 0
((-5 * 4 + 4i * 4) + -3i * (-5 + 4i)) = 0
((-20 + 16i) + -3i * (-5 + 4i)) = 0
(-20 + 16i + (-5 * -3i + 4i * -3i)) = 0
(-20 + 16i + (15i + -12i2)) = 0

Combine like terms: 16i + 15i = 31i
(-20 + 31i + -12i2) = 0

Solving
-20 + 31i + -12i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-4 + 3i)(5 + -4i) = 0


Subproblem 1
Set the factor '(-4 + 3i)' equal to zero and attempt to solve:

Simplifying
-4 + 3i = 0

Solving
-4 + 3i = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3i = 0 + 4
3i = 0 + 4

Combine like terms: 0 + 4 = 4
3i = 4

Divide each side by '3'.
i = 1.333333333

Simplifying
i = 1.333333333

Subproblem 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Solution
i = {1.333333333, 1.25}

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