Show that x = 3 + 4/ is a solution to the equation x2 6x + 25 = 0. We will first substitute 3 + 4i for x in the left side of the equation. Then simplify powers of i and combine like terms to verify that it equals the right side of the equation. ])•: x² - 6x + 25 = 25 - (* - - 16/2) - 18 - 24i + 25 + 16 18 + 25) + (24i – 24i) + 6) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 54E
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Show that x = 3 + 4i is a solution to the equation x2 – 6x + 25 = 0.
We will first substitute 3 + 4i for x in the left side of the equation. Then simplify powers of i and combine like terms to verify that it equals the right side of the equation.
x² – 6x + 25 =
+ 25
- (» -|
|+ 107) - 18 - 20 - 25
- 18 - 24i + 25
- (9 + 10
18 + 25) + (24i – 24i)
= 0
Transcribed Image Text:Show that x = 3 + 4i is a solution to the equation x2 – 6x + 25 = 0. We will first substitute 3 + 4i for x in the left side of the equation. Then simplify powers of i and combine like terms to verify that it equals the right side of the equation. x² – 6x + 25 = + 25 - (» -| |+ 107) - 18 - 20 - 25 - 18 - 24i + 25 - (9 + 10 18 + 25) + (24i – 24i) = 0
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