(4+5i)(4+i)=

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Solution for (4+5i)(4+i)= equation:


Simplifying
(4 + 5i)(4 + i) = 0

Multiply (4 + 5i) * (4 + i)
(4(4 + i) + 5i * (4 + i)) = 0
((4 * 4 + i * 4) + 5i * (4 + i)) = 0
((16 + 4i) + 5i * (4 + i)) = 0
(16 + 4i + (4 * 5i + i * 5i)) = 0
(16 + 4i + (20i + 5i2)) = 0

Combine like terms: 4i + 20i = 24i
(16 + 24i + 5i2) = 0

Solving
16 + 24i + 5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + i)(4 + 5i) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8

Solution

i = {-4, -0.8}

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