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Transcript
Name _____________________ Date _________________________ Calculating Distance in the Complex Plane - Step-by-Step Lesson What is the distance between (2 +1i) and (6 + 5i) on the complex plane? Explanation: y 6 5 4 3 2 x 1 1 2 3 4 5 6 ‐6 ‐5 ‐4 ‐3 ‐2 ‐1 ‐1 ‐2 ‐3 ‐4 ‐5 Step 1) Graph the points and connect them with a line, shown above. The xaxis represents the real numbers and the y-axis represents the imaginary numbers. For example: (2 + 1i) translates to the rectangular coordinates (2, 1) 2 (real number) = x 1i (imaginary number) = y Step 2) Use the Pythagorean theorem, count the columns and find the length of two points - the imaginary number and the real number. Calculate distance in the complex plane. It would take 4 moves down and 4 moves right to create a triangle. Step 3) √42+42 =5.65 (Solve the Pythagorean theorem) The distance is 5.65. Tons of Free Math Worksheets at: © www.mathworksheetsland.com
