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

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


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

Multiply (2 + -3i) * (5 + -7i)
(2(5 + -7i) + -3i * (5 + -7i)) = 0
((5 * 2 + -7i * 2) + -3i * (5 + -7i)) = 0
((10 + -14i) + -3i * (5 + -7i)) = 0
(10 + -14i + (5 * -3i + -7i * -3i)) = 0
(10 + -14i + (-15i + 21i2)) = 0

Combine like terms: -14i + -15i = -29i
(10 + -29i + 21i2) = 0

Solving
10 + -29i + 21i2 = 0

Solving for variable 'i'.

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

Subproblem 1

Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667

Subproblem 2

Set the factor '(5 + -7i)' equal to zero and attempt to solve: Simplifying 5 + -7i = 0 Solving 5 + -7i = 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 + -7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7i = 0 + -5 -7i = 0 + -5 Combine like terms: 0 + -5 = -5 -7i = -5 Divide each side by '-7'. i = 0.7142857143 Simplifying i = 0.7142857143

Solution

i = {0.6666666667, 0.7142857143}

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