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

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


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

Multiply (7 + 3i) * (-5 + -3i)
(7(-5 + -3i) + 3i * (-5 + -3i)) = 0
((-5 * 7 + -3i * 7) + 3i * (-5 + -3i)) = 0
((-35 + -21i) + 3i * (-5 + -3i)) = 0
(-35 + -21i + (-5 * 3i + -3i * 3i)) = 0
(-35 + -21i + (-15i + -9i2)) = 0

Combine like terms: -21i + -15i = -36i
(-35 + -36i + -9i2) = 0

Solving
-35 + -36i + -9i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 36i + 9i2) = 0

Factor a trinomial.
-1((7 + 3i)(5 + 3i)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + 3i)' equal to zero and attempt to solve:

Simplifying
5 + 3i = 0

Solving
5 + 3i = 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 + 3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3i = 0 + -5
3i = 0 + -5

Combine like terms: 0 + -5 = -5
3i = -5

Divide each side by '3'.
i = -1.666666667

Simplifying
i = -1.666666667
Solution
i = {-2.333333333, -1.666666667}

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