/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 Evaluate \(x^{2}-2 x+5\) for \(x... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 52

Evaluate \(x^{2}-2 x+5\) for \(x=1-2 i\)

Short Answer

Expert verified
The solution to the expression \(x^{2} - 2x + 5\) when evaluated for \(x = 1-2i\) is 0.

Step by step solution

01

Substituting the value of x

First, we substitute \(x = 1 - 2i\) into the given polynomial \(x^{2}-2 x+5\) to get \((1 - 2i)^{2} - 2*(1 - 2i) + 5\).
02

Simplifying the Expression

To simplify this, start by expanding the first term \((1 - 2i)^{2}\), square each term and then cross multiply. The result is \(1 - 4i + 4i^{2}\). The second term becomes \(-2 + 4i\). Finally, add 5. The expression then becomes \(1 - 4i + 4i^{2} - 2 + 4i + 5\).
03

Continue to Simplify Using \(i^{2}=-1\)

We know that \(i^{2}=-1\). With this, the above expression becomes \(1 - 4i + 4*(-1) - 2 + 4i + 5 = 1 - 2 + 5 - 4\).

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