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

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


Simplifying
(2 + 5i)(7 + -1i) = 0

Multiply (2 + 5i) * (7 + -1i)
(2(7 + -1i) + 5i * (7 + -1i)) = 0
((7 * 2 + -1i * 2) + 5i * (7 + -1i)) = 0
((14 + -2i) + 5i * (7 + -1i)) = 0
(14 + -2i + (7 * 5i + -1i * 5i)) = 0
(14 + -2i + (35i + -5i2)) = 0

Combine like terms: -2i + 35i = 33i
(14 + 33i + -5i2) = 0

Solving
14 + 33i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7 + -1i)(2 + 5i) = 0

Subproblem 1

Set the factor '(7 + -1i)' equal to zero and attempt to solve: Simplifying 7 + -1i = 0 Solving 7 + -1i = 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 + -1i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1i = 0 + -7 -1i = 0 + -7 Combine like terms: 0 + -7 = -7 -1i = -7 Divide each side by '-1'. i = 7 Simplifying i = 7

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 = {7, -0.4}

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