=j 2 + (−1)+ (−j2)+ 5
=j 2 +−j 2 + (−1)+ 5
= 0 + 4
= 4
Our third solution is (x,y) = (−j, 4).
And finally ...
Now it’s time to check these solutions to be sure that they work. I can’t blame you if you’re
weary of doing arithmetic, and you’d prefer to take these solutions on faith. That’s all right
for now. Tomorrow, when your mind is rested, come back and check them for complemen-
tary credit.
Practice Exercises
This is an open-book quiz. You may (and should) refer to the text as you solve these problems.
Don’t hurry! You’ll find worked-out answers in App. C. The solutions in the appendix may
not represent the only way a problem can be figured out. If you think you can solve a particu-
lar problem in a quicker or better way than you see there, by all means try it!
- Solve the following pair of equations as a two-by-two system, including the complex-
number solutions, if any. Let x be the independent variable, and then define y as a
function of x in each equation:
3 x+y− 1 = 0
and
2 x^2 −y+ 1 = 0
- Check the solution(s) to Prob. 1 in the original equations for correctness.
- Solve the following pair of equations as a two-by-two system, including the complex-
number solutions, if any. Let x be the independent variable, and then define y as a
function of x in each equation:
3 x+y− 1 = 0
and
2 x^2 − 3 x−y+ 3 = 0
- Check the solution(s) to Prob. 3 in the original equations for correctness.
Practice Exercises 461
