(9-4i)(2+9i)=

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Solution for (9-4i)(2+9i)= equation:


Simplifying
(9 + -4i)(2 + 9i) = 0

Multiply (9 + -4i) * (2 + 9i)
(9(2 + 9i) + -4i * (2 + 9i)) = 0
((2 * 9 + 9i * 9) + -4i * (2 + 9i)) = 0
((18 + 81i) + -4i * (2 + 9i)) = 0
(18 + 81i + (2 * -4i + 9i * -4i)) = 0
(18 + 81i + (-8i + -36i2)) = 0

Combine like terms: 81i + -8i = 73i
(18 + 73i + -36i2) = 0

Solving
18 + 73i + -36i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(9 + -4i)(2 + 9i) = 0

Subproblem 1

Set the factor '(9 + -4i)' equal to zero and attempt to solve: Simplifying 9 + -4i = 0 Solving 9 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4i = 0 + -9 -4i = 0 + -9 Combine like terms: 0 + -9 = -9 -4i = -9 Divide each side by '-4'. i = 2.25 Simplifying i = 2.25

Subproblem 2

Set the factor '(2 + 9i)' equal to zero and attempt to solve: Simplifying 2 + 9i = 0 Solving 2 + 9i = 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 + 9i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9i = 0 + -2 9i = 0 + -2 Combine like terms: 0 + -2 = -2 9i = -2 Divide each side by '9'. i = -0.2222222222 Simplifying i = -0.2222222222

Solution

i = {2.25, -0.2222222222}

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