 2.4.1: Fill in the blanks. A ________ number has the form where
 2.4.2: Fill in the blanks. An ________ number has the form where
 2.4.3: Fill in the blanks. A ________ ________ number has the form where
 2.4.4: Fill in the blanks. The imaginary unit is defined as ________, wher...
 2.4.5: Fill in the blanks. When is a positive real number, the ________ __...
 2.4.6: Fill in the blanks. The numbers and are called ________ ________, a...
 2.4.7: Equality of Complex Numbers In Exercises 710, find real numbers and...
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 2.4.11: Writing a Complex Number in Standard Form In Exercises 1122, write ...
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 2.4.43: Multiplying Conjugates In Exercises 4350, write the complex conjuga...
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 2.4.91: Impedance The opposition to current in an electrical circuit is cal...
 2.4.92: Cube of a Complex Number Cube each complex number.
 2.4.93: True or False? In Exercises 9396, determine whether the statement i...
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 2.4.97: Pattern Recognition Complete the following. What pattern do you see...
 2.4.98: HOW DO YOU SEE IT? The coordinate system shown below is called the ...
 2.4.99: Error Analysis Describe the error.
 2.4.100: Proof Prove that the complex conjugate of the product of two comple...
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Solutions for Chapter 2.4: Complex Numbers
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 2.4: Complex Numbers
Get Full SolutionsChapter 2.4: Complex Numbers includes 101 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3. Since 101 problems in chapter 2.4: Complex Numbers have been answered, more than 34758 students have viewed full stepbystep solutions from this chapter. Precalculus with Limits was written by and is associated to the ISBN: 9781133947202.

Boundary
The set of points on the “edge” of a region

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Factored form
The left side of u(v + w) = uv + uw.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Imaginary part of a complex number
See Complex number.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Line of symmetry
A line over which a graph is the mirror image of itself

Logarithm
An expression of the form logb x (see Logarithmic function)

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Normal distribution
A distribution of data shaped like the normal curve.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Polar axis
See Polar coordinate system.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Symmetric property of equality
If a = b, then b = a

Tree diagram
A visualization of the Multiplication Principle of Probability.

Unit vector
Vector of length 1.