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NAME
4-4
DATE
PERIOD
Word Problem Practice
Complex Numbers
1. SIGN ERRORS Jennifer and Jessica
come up with different answers to the
same problem. They had to multiply
(4 + i)(4 – i) and give their answer as
a complex number. Jennifer claims that
the answer is 15 and Jessica claims that
the answer is 17. Who is correct? Explain.
4. ROTATIONS Complex numbers can
be used to perform rotations in the plane.
For example, if (x, y) are the coordinates
of a point in the plane, then the real and
imaginary parts of i(x + yi) are the
horizontal and vertical coordinates of the
90° counterclockwise rotation of (x, y)
about the origin. What are the real and
imaginary parts of i(x + yi)?
2. COMPLEX CONJUGATES You
have seen that the product of complex
conjugates is always a real number.
Show that the sum of complex
conjugates is also always a real number.
5. ELECTRICAL ENGINEERING
Alternating current (AC) in an electrical
circuit can be described by complex
numbers. In any electrical circuit, Z, the
impedance in the circuit, is related to the
voltage V and the current I by the formula
𝑉
Z = . The standard electrical voltage in
𝐼
Europe is 220 volts, so in these problems
use V = 220.
3. PYTHAGOREAN TRIPLES If three
integers a, b, and c satisfy a2 + b2 = c2, then
they are called a Pythagorean triple.
Suppose that a, b, and c are a Pythagorean
triple. Show that the real and imaginary
parts of (a + bi)2, together with the number
c2, form another Pythagorean triple.
a. Find the impedance in a standard
European circuit if the current is
22 – 11i amps.
b. Find the current in a standard
European circuit if the impedance
is 10 – 5i watts.
c. Find the impedance in a standard
European circuit if the current is
20i amps.
Chapter 4
28
Glencoe Algebra 2