(2+3i)(4-i)=0

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Solution for (2+3i)(4-i)=0 equation: 


Simplifying
(2 + 3i)(4 + -1i) = 0

Multiply (2 + 3i) * (4 + -1i)
(2(4 + -1i) + 3i * (4 + -1i)) = 0
((4 * 2 + -1i * 2) + 3i * (4 + -1i)) = 0
((8 + -2i) + 3i * (4 + -1i)) = 0
(8 + -2i + (4 * 3i + -1i * 3i)) = 0
(8 + -2i + (12i + -3i2)) = 0

Combine like terms: -2i + 12i = 10i
(8 + 10i + -3i2) = 0

Solving
8 + 10i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -1i)(2 + 3i) = 0


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

Simplifying
4 + -1i = 0

Solving
4 + -1i = 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 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4

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 = {4, -0.6666666667}

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