189 CHAPTER 1 Test Prep Concepts Examples Step 2 Assign a variable. Step 3 Write an equation. Step 4 Solve the equation. Step 5 State the answer. Step 6 Check. Let x = the number of liters of 30% solution. 50 - x = the number of liters of 80% solution. Summarize the information of the problem in a table. In the complex number -6 + 2i, the real part is -6 and the imaginary part is 2. Simplify. 2 -4 = 2i 2 -12 = i212 = i24 # 3 = 2i23 Perform the operations. 12 + 3i2 + 13 + i2 - 12 - i2 = 12 + 3 - 22 + 13 + 1 + 12i = 3 + 5i 16 + i213 - 2i2 = 18 - 12i + 3i - 2i2 FOIL method = 118 + 22 + 1-12 + 32i i2 = -1 = 20 - 9i Strength Liters of Solution Liters of Pure Alcohol 30% x 0.30x 80% 50 - x 0.80150 - x2 50% 50 0.501502 The equation is 0.30x + 0.80150 - x2 = 0.501502. Solve the equation to obtain x = 30. Therefore, 30 L of the 30% solution and 50 - 30 = 20L of the 80% solution must be mixed. CHECK 0.301302 + 0.80150 - 302≟0.501502 25 = 25 ✓ True 1.3 Complex Numbers Definition of i i =!−1, and therefore, i2 = −1 Definition of Complex Number (a and b real) a + bi Real Imaginary part part Definition of !−a For a 70, !−a =i!a. Adding and Subtracting Complex Numbers Add or subtract the real parts, and add or subtract the imaginary parts. Multiplying and Dividing Complex Numbers Multiply complex numbers as with binomials, and use the fact that i2 = -1.
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