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

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


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

Multiply (7 + 2i) * (2 + -5i)
(7(2 + -5i) + 2i * (2 + -5i)) = 0
((2 * 7 + -5i * 7) + 2i * (2 + -5i)) = 0
((14 + -35i) + 2i * (2 + -5i)) = 0
(14 + -35i + (2 * 2i + -5i * 2i)) = 0
(14 + -35i + (4i + -10i2)) = 0

Combine like terms: -35i + 4i = -31i
(14 + -31i + -10i2) = 0

Solving
14 + -31i + -10i2 = 0

Solving for variable 'i'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 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 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5

Solution

i = {0.4, -3.5}

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