=(1+-3i)*(-2+5i)

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Solution for =(1+-3i)*(-2+5i) equation: 


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

Multiply (1 + -3i) * (-2 + 5i)
0 = (1(-2 + 5i) + -3i * (-2 + 5i))
0 = ((-2 * 1 + 5i * 1) + -3i * (-2 + 5i))
0 = ((-2 + 5i) + -3i * (-2 + 5i))
0 = (-2 + 5i + (-2 * -3i + 5i * -3i))
0 = (-2 + 5i + (6i + -15i2))

Combine like terms: 5i + 6i = 11i
0 = (-2 + 11i + -15i2)

Solving
0 = -2 + 11i + -15i2

Solving for variable 'i'.

Combine like terms: 0 + 2 = 2
2 + -11i + 15i2 = -2 + 11i + -15i2 + 2 + -11i + 15i2

Reorder the terms:
2 + -11i + 15i2 = -2 + 2 + 11i + -11i + -15i2 + 15i2

Combine like terms: -2 + 2 = 0
2 + -11i + 15i2 = 0 + 11i + -11i + -15i2 + 15i2
2 + -11i + 15i2 = 11i + -11i + -15i2 + 15i2

Combine like terms: 11i + -11i = 0
2 + -11i + 15i2 = 0 + -15i2 + 15i2
2 + -11i + 15i2 = -15i2 + 15i2

Combine like terms: -15i2 + 15i2 = 0
2 + -11i + 15i2 = 0

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


Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve:

Simplifying
1 + -3i = 0

Solving
1 + -3i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3i = 0 + -1
-3i = 0 + -1

Combine like terms: 0 + -1 = -1
-3i = -1

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333

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

Simplifying
2 + -5i = 0

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

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

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

Divide each side by '-5'.
i = 0.4

Simplifying
i = 0.4
Solution
i = {0.3333333333, 0.4}

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