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

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


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

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

Combine like terms: 5i + 21i = 26i
(35 + 26i + 3i2) = 0

Solving
35 + 26i + 3i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(7 + i)' equal to zero and attempt to solve:

Simplifying
7 + i = 0

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

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

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

Simplifying
i = -7

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 = {-7, -1.666666667}

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