PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form o…
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Chapter P.6, Problem 46E
Solution

The expression is true or false i, i+i2+i3+i4=0 justify your answer.

True

Given:

The expression, i, i+i2+i3+i4=0 .

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 i, i+i2+i3+i4=0 is true or false , lfirst solving the expression as shown below:

  i, i+i2+i3+i4=0we know  that i2=−1,  i3=−i,  i4=1i, i+−1+−i+1=0i,i−1−i+1=0i=o

So, the expression for the complex number is true.

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Chapter P.6, Problem 45E
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Chapter P.6, Problem 47E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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