Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 365: 119

Answer

Since -2 + i satisfies the equation $x^2 + 4x + 5 = 0$, it is a solution of the equation.

Work Step by Step

For -2 + i to be a solution of the equation $x^2 + 4x + 5 = 0$, -2 + i should satisfy the equation. Substitute $x=-2 + i$ into $x^2 + 4x + 5$, we have $(-2+i)^2 + 4(-2+i) + 5$ = $4 -4i +i^2 -8 + 4i + 5$ = $1 + i^2$ = $1 - 1$ $(i^2 = -1)$ = $0$ = R.H.S Therefore, -2 + i is a solution of the equation $x^2 + 4x + 5 = 0$.
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