(7+3i)(5+2i)=

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Solution for (7+3i)(5+2i)= equation: 


Simplifying
(7 + 3i)(5 + 2i) = 0

Multiply (7 + 3i) * (5 + 2i)
(7(5 + 2i) + 3i * (5 + 2i)) = 0
((5 * 7 + 2i * 7) + 3i * (5 + 2i)) = 0
((35 + 14i) + 3i * (5 + 2i)) = 0
(35 + 14i + (5 * 3i + 2i * 3i)) = 0
(35 + 14i + (15i + 6i2)) = 0

Combine like terms: 14i + 15i = 29i
(35 + 29i + 6i2) = 0

Solving
35 + 29i + 6i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + 2i)(7 + 3i) = 0


Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 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 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5

Subproblem 2
Set the factor '(7 + 3i)' equal to zero and attempt to solve:

Simplifying
7 + 3i = 0

Solving
7 + 3i = 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 + 3i = 0 + -7

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

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

Divide each side by '3'.
i = -2.333333333

Simplifying
i = -2.333333333
Solution
i = {-2.5, -2.333333333}

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