ࡱ> *,)_ tbjbj 4@5\5\t.....BBBBL\B$8|7777777$9V<7.7..7..77R'470F;s/5770$895<5.><77<=D.7t77c.$8>> : Investigation: Applying Complex Numbers When working with complex numbers, the rules are similar to those you use when working with real numbers. Part 1: Add these complex numbers. (Hint: its just like adding like terms) a. (2 4i) + (3 + 5i) b. (7 + 2i) + (-2 + i) c. (2 4i) (3 + 4i) d. (4 -4i) (1 3i) Part 2: Now multiply these binomials. Express your products in the form a + bi. (Hint: Use FOIL, use the fact that i2 = -1, and then combine like terms) (2 4i)(3 + 5i) b. (7 + 2i)(-2 + i) c. (2 4i)2 d. (4 4i)(1 -3i) Part 3: The conjugate of a + bi is a bi. Lets see what happens when we add or subtract them together. (2 4i) + (2 + 4i) b. (7 + 2i) + (7 2i) c. (2 4i)(2 + 4i) d. (-4 + 4i)(-4 4i) State what happens when we multiply (or add) with conjugates: ______________________________ Part 4: Recall rationalizing the denominator with radicals  EMBED Equation.3  We will use a similar technique to change the complex denominator to a real number by using conjugates. Once you have a real number in the denominator, divide to get an answer in the form a + bi. (Hint: Multiply the conjugate of the denominator to the top and bottom part of the fraction. FOIL the top and bottom and simplify. Then simplify the fraction itself.) a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  Practice 7-5 Add or subtract (5 1i) + (3 + 5i) b. (6 + 2i) (-1 + 2i) c. (2 + 3i) + (2 5i) d. (2.35 + 2.71i) (4.91 + 3.32i) Multiply. (5 1i)(3 + 5i) b. 6(-1 + 2i) c. 3i(2 5i) d. (2.35 + 2.71i)(4.91 + 3.32i) Find the conjugate of each complex number. 5 i b. -1 + 2i c. 2 + 3i d. -2.35 2.71i Draw Venn diagrams to show the relationships between these sets of numbers. Real number and complex numbers. Rational numbers and irrational numbers Imaginary numbers and complex numbers Imaginary numbers and real numbers Complex numbers, real numbers, and imaginary numbers Rewrite this quadratic equation in general form. [x (2+i)][x (2 i)] = 0 Rewrite the quotient  EMBED Equation.3  in the form a + bi. Solve each equation. Use substitution to check your solutions. Label each solution as real, imaginary, and/or complex. x2 1 =0 b. x2 + 1 = 0 c. x2 4x + 6 = 0 d. x2 + x = -1 e. -2x2 + 4x = 3 Name: _______________________ Date: ___________ Homework 7.5 Part 2 Complex Arithmetic 1. Simplify the following. Put your answer in the form a + bi a. 2.3 EMBED Equation.3  b.  EMBED Equation.3  c. (-5 + 6i) (1 i) d. (-2.4 5.6i) + 5.9 + 1.8i) e. (2.5 + 1.5i)(3.4 0.6i) f.  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