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

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Solution for (3+5i)(2-7i)=0 equation:


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

Multiply (3 + 5i) * (2 + -7i)
(3(2 + -7i) + 5i * (2 + -7i)) = 0
((2 * 3 + -7i * 3) + 5i * (2 + -7i)) = 0
((6 + -21i) + 5i * (2 + -7i)) = 0
(6 + -21i + (2 * 5i + -7i * 5i)) = 0
(6 + -21i + (10i + -35i2)) = 0

Combine like terms: -21i + 10i = -11i
(6 + -11i + -35i2) = 0

Solving
6 + -11i + -35i2 = 0

Solving for variable 'i'.

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

Subproblem 1

Set the factor '(2 + -7i)' equal to zero and attempt to solve: Simplifying 2 + -7i = 0 Solving 2 + -7i = 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 + -7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7i = 0 + -2 -7i = 0 + -2 Combine like terms: 0 + -2 = -2 -7i = -2 Divide each side by '-7'. i = 0.2857142857 Simplifying i = 0.2857142857

Subproblem 2

Set the factor '(3 + 5i)' equal to zero and attempt to solve: Simplifying 3 + 5i = 0 Solving 3 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5i = 0 + -3 5i = 0 + -3 Combine like terms: 0 + -3 = -3 5i = -3 Divide each side by '5'. i = -0.6 Simplifying i = -0.6

Solution

i = {0.2857142857, -0.6}

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