Find each power of i. See Example 8.
85.A student simplified as follows:
Explain the mathematical justification for this correct work.86.Explain why
and
must be equal. (Do not actually perform the computation.)Ohm’s lawfor the current I in a circuit with voltage E, resistance R, capacitive reactance
and inductive reactance is
Use this law to work Exercises 87 and 88.
87.Find Iif and
88.Find Eif and
Complex numbers will appear again in this book in Chapter 9,when we study quadratic
equations. The following exercises examine how a complex number can be a solution of a
quadratic equation.
89.Show that is a solution of
Then show that its conjugate is also a solution.90.Show that is a solution of
Then show that its conjugate is also a solution.Brain Busters Perform the indicated operations. Give answers in standard form.
93. 94.
Solve each equation. See Sections 2.1 and 6.5.
- 5 x^2 - 3 x= 2 100.- 6 x^2 + 7 x=- 10
x 1 x+ 32 = 40 2 x^2 - 5 x- 7 = 06 x+ 13 = 0 4 x- 7 = 0PREVIEW EXERCISES
a4 - i
1 +i-
2 i
2 +ia b 4 i2 +i
2 - i+
i
1 +ibi2
3 + 4 i+
4
1 - i3
2 - i+
5
1 +ix^2 - 6 x+ 13 =0.3 + 2 ix^2 - 2 x+ 26 =0.1 + 5 iI= 1 - i, R=2, XL=3, Xc=1.E= 2 + 3 i, R=5, XL=4, Xc=3.I=
E
R+ 1 XL-Xc 2 i.
XL
Xc,146 + 25 i 213 - 6 i 2 146 + 25 i 213 - 6 i 2 i^12i-^18 =i-^18 #i^20 =i-^18 +^20 =i^2 =-1.
i-^18i^102 i^43 i^83 i-^5 i-^17i^18 i^26 i^89 i^48 i^38