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

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


Simplifying
(5 + 3i)(2 + -1i) = 0

Multiply (5 + 3i) * (2 + -1i)
(5(2 + -1i) + 3i * (2 + -1i)) = 0
((2 * 5 + -1i * 5) + 3i * (2 + -1i)) = 0
((10 + -5i) + 3i * (2 + -1i)) = 0
(10 + -5i + (2 * 3i + -1i * 3i)) = 0
(10 + -5i + (6i + -3i2)) = 0

Combine like terms: -5i + 6i = 1i
(10 + 1i + -3i2) = 0

Solving
10 + 1i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -1i)(5 + 3i) = 0


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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2

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, -1.666666667}

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