(2+3i)(7-4i)=

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Solution for (2+3i)(7-4i)= equation: 


Simplifying
(2 + 3i)(7 + -4i) = 0

Multiply (2 + 3i) * (7 + -4i)
(2(7 + -4i) + 3i * (7 + -4i)) = 0
((7 * 2 + -4i * 2) + 3i * (7 + -4i)) = 0
((14 + -8i) + 3i * (7 + -4i)) = 0
(14 + -8i + (7 * 3i + -4i * 3i)) = 0
(14 + -8i + (21i + -12i2)) = 0

Combine like terms: -8i + 21i = 13i
(14 + 13i + -12i2) = 0

Solving
14 + 13i + -12i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7 + -4i)(2 + 3i) = 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 '(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 = {1.75, -0.6666666667}

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