Algebra Know-It-ALL
Part Two 345 Question 19-8 Suppose that we play the matrix morphing game in an attempt to solve a three-by-three linear system, ...
This page intentionally left blank ...
PART 3 Nonlinear Equations and Relations Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. ...
This page intentionally left blank ...
349 CHAPTER 21 Imaginary and Complex Numbers All the algebra we’ve done so far has been of the first degree. Variables were neve ...
350 Imaginary and Complex Numbers you’re more likely to go into science or engineering than pure mathematics, so you should get ...
And the 6th: j^6 =j^5 ×j =j×j =j^2 =− 1 Can you see what will happen if we keep going like this, increasing the integer power by ...
352 Imaginary and Complex Numbers Relative and absolute values Imagine a “number reflector” plane, like a mathematical mirror, p ...
In general, if b is any nonnegative real number, then |jb|=b and |−jb|=b To add, move upward Think of upward distances on the im ...
354 Imaginary and Complex Numbers of−3 units is the same as a downward displacement of 3 units. This process is shown on the rig ...
move down by −5 units, which means we really move up by 5 units. We finish at the point corresponding toj2. We can write −j 3 − ...
356 Imaginary and Complex Numbers − 5 −j 3 1 −j 6 0 + j0 When a complex number is written as a difference between a real number ...
quantities that are part real and part imaginary. The real part is expressed toward the right for positive and toward the left f ...
358 Imaginary and Complex Numbers a complex-number division problem, you can use the following formula. If a,b,c, and d are real ...
Let’s find the absolute value of 3 −j4. In this case, a= 3 and b=−4. Squaring both of these and adding the results gives us 32 + ...
360 Imaginary and Complex Numbers The line segment connecting (3, j ) and (5, j 4) is opposite from the side with slope m 1. Let ...
Those two opposite sides are also parallel. This proves that the quadrilateral in Fig. 21-5 is a paral- lelogram. Here’s an extr ...
362 Imaginary and Complex Numbers Find the quotient (a+jb)/(a−jb), assuming that a and b are not both equal to 0. Find the quot ...
363 CHAPTER 22 Quadratic Equations with Real Roots In this chapter, you’ll learn about single-variable quadratic equations, ofte ...
364 Quadratic Equations with Real Roots As you know, all cases of subtraction are sums in disguise. The above expressions can be ...
«
14
15
16
17
18
19
20
21
22
23
»
Free download pdf