Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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