(5+3i)(9+8i)=45

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Solution for (5+3i)(9+8i)=45 equation:


Simplifying
(5 + 3i)(9 + 8i) = 45

Multiply (5 + 3i) * (9 + 8i)
(5(9 + 8i) + 3i * (9 + 8i)) = 45
((9 * 5 + 8i * 5) + 3i * (9 + 8i)) = 45
((45 + 40i) + 3i * (9 + 8i)) = 45
(45 + 40i + (9 * 3i + 8i * 3i)) = 45
(45 + 40i + (27i + 24i2)) = 45

Combine like terms: 40i + 27i = 67i
(45 + 67i + 24i2) = 45

Add '-45' to each side of the equation.
45 + 67i + -45 + 24i2 = 45 + -45

Reorder the terms:
45 + -45 + 67i + 24i2 = 45 + -45

Combine like terms: 45 + -45 = 0
0 + 67i + 24i2 = 45 + -45
67i + 24i2 = 45 + -45

Combine like terms: 45 + -45 = 0
67i + 24i2 = 0

Solving
67i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i'.
i(67 + 24i) = 0

Subproblem 1

Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0

Subproblem 2

Set the factor '(67 + 24i)' equal to zero and attempt to solve: Simplifying 67 + 24i = 0 Solving 67 + 24i = 0 Move all terms containing i to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + 24i = 0 + -67 Combine like terms: 67 + -67 = 0 0 + 24i = 0 + -67 24i = 0 + -67 Combine like terms: 0 + -67 = -67 24i = -67 Divide each side by '24'. i = -2.791666667 Simplifying i = -2.791666667

Solution

i = {0, -2.791666667}

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