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

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


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

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

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

Solving
14 + 29i + -15i2 = 0

Solving for variable 'i'.

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


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 '(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 = {2.333333333, -0.4}

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