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Name:__________________________ Date:___________________ Mr. Nickels Math 3C Imaginary Numbers Homework 1 Expressed in simplest form, i16 i 6 2i 5 i13 is equivalent to (1) 1 (3) i (2) -1 (4) -i 2 When simplified, i 27 i 34 is equal to (1) i (3) i 1 61 (2) i (4) i 1 3 What is the value of i 99 i 3 ? (1) 1 (3) i (2) i 96 (4) 0 4 What is the sum of 2 and 18 ? (1) 5 i 2 (3) 2i 5 5 6 7 8 (2) 4i 2 (4) 6i The expression i 0 i1 i 2 i 3 i 4 is equal to (1) 1 (3) i (2) -1 (b)-i i 16 The expression 3 is equivalent to i (1) 1 (3) i (2) -1 (4) –i What is the multiplicative inverse of 3i? 1 (1) -3i (3) 3 i (2) -3 (4) 3 Mrs. Donahue made up a game to help her class learn about imaginary numbers. The winner will be the student whose expression is equivalent to -i. Which expression will win the game? (1) i 46 (3) i 48 (2) i 47 (4) i 49 48 35 . 25 27 in simplest a + bi form. 9 Express 10 What is the sum of 2 4 and 3 16 expressed in a + bi form? (1) 1 2i (3) 1 12i (2) 1 i 20 (4) 14 i What is the product of 5 36 , and 1 49 , expressed in simplest a + bi form? (1) –37 + 41i (3) 47 + 41i (2) 5 – 71i (4) 47 – 29i 11 18 When expressed as a monomial in terms of i, 2 32 5 8 is equivalent to (1) 2 2i (3) 2i 2 (2) 2i 2 (4) 18i 2 The expression ( 1 i ) 3 is equivalent to (1) –3i (3) –1 – i (2) –2 – 2i (4) 2 + 2i 3 If f ( x) x 2 x 2 , then f (i ) is equivalent to (1) –2 + i (3) 2 + i (2) –2 – i (4) 2 – i 2i The expression is equivalent to 3i 6 5i 7 5i (1) (3) 8 10 6i 7i (2) (4) 8 10 What is the value of x in the equation 5 2 x 3i ? (1) 1 (3) –2 (2) 7 (4) 4 Melissa and Joe are playing a game with complex numbers. If Melissa has a score of 5 – 4i and Joe has a score of 3 + 2i, what is their total score? (1) 8 + 6i (3) 8 – 6i (2) 8 + 2i (4) 8 – 2i Show that the product of a + bi and its conjugate is a real number. 19 The complex number c di is equal to (2 i) 2 . What is the value of c? 20 In an electrical circuit, the voltage, E, in volts, the current, I, in amps, and the opposition to the flow of current, called impedance, Z, in ohms, are related by the equation E = IZ. A circuit has a current of (3 + i) amps and an impedance of (–2 + i) ohms. Determine the voltage in a + bi form. 21 The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of this circuit? (1) 8 + i (3) 4 + i (2) 8 + 7i (4) 4 – i 12 13 14 15 16 17 22 Impedance measures the opposition of an electrical circuit to the flow of electricity. The total impedance in a particular circuit is given by the formula ZZ ZT 1 2 . What is the total impedance of a circuit, ZT , if Z1 1 2i and Z1 Z2 Z2 1 2i ? 5 (1) 1 (3) 2 3 (2) 0 (4) 2 Answers: 1) 4 2) 3 3) 4 4) 2 5) 1 6) 3 7) 4 8) 2 9) 8.5 + 7Isqr3 10) 1 11) 4 12) 3 13) 4 14) 4 15) 4 16) 2 17) 4 18) (a+bi)(a-bi) = a^2+b^2 19) 3 20) -7+I 21) 1 22) 3