(4+3i)(7+6i)=

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Solution for (4+3i)(7+6i)= equation: 


Simplifying
(4 + 3i)(7 + 6i) = 0

Multiply (4 + 3i) * (7 + 6i)
(4(7 + 6i) + 3i * (7 + 6i)) = 0
((7 * 4 + 6i * 4) + 3i * (7 + 6i)) = 0
((28 + 24i) + 3i * (7 + 6i)) = 0
(28 + 24i + (7 * 3i + 6i * 3i)) = 0
(28 + 24i + (21i + 18i2)) = 0

Combine like terms: 24i + 21i = 45i
(28 + 45i + 18i2) = 0

Solving
28 + 45i + 18i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + 3i)(7 + 6i) = 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 '(7 + 6i)' equal to zero and attempt to solve:

Simplifying
7 + 6i = 0

Solving
7 + 6i = 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 + 6i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6i = 0 + -7
6i = 0 + -7

Combine like terms: 0 + -7 = -7
6i = -7

Divide each side by '6'.
i = -1.166666667

Simplifying
i = -1.166666667
Solution
i = {-1.333333333, -1.166666667}

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