Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
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Chapter P.6, Problem 45E
Solution

The expression is true or false z=−z¯ , justify your answer

False

Given:

The expression, z=−z¯ .

Concept used:

  • Product of powers property, an⋅am=an+m
  • FOIL to multiply binomials, a+bc+d=a⋅c+a⋅d+b⋅c+b⋅d
  • Properties of complex number: −1=i, i2=−1, i3=−i
  • The complex conjugate of a+bi is a−bi .
  • Difference of squares formula, a+ba−b=a2−b2
  • Properties of complex number: x+iy¯=x−iy

Calculation:

In order to justify that the expression z=−z¯ is true or false , let z=x+iy by putting the value of z in the given expression solving the expression as shown below:

  z=−z¯x+iy=−x+iy¯x+iy=−x−iyx+iy=−x+iyadd x both side 2x+iy=iysubtract iy from both side2x=0x=0

So, the real part of z is zero only imaginary part exits, therefore the expression is false .

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Chapter P.6, Problem 44E
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Chapter P.6, Problem 46E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

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