Solve the Absolute Value Equation: |z - 7| = 3

Question

Find the value of z z such that z7=3 |z - 7| = 3 .

Step-by-Step Solution

Given the equation z7=3 |z - 7| = 3 , consider the two cases for the absolute value:

  1. Case 1: z7=3z - 7 = 3
    Add 7: z=10z = 10.
  2. Case 2: z7=3z - 7 = -3
    Add 7: z=4z = 4.

Thus, zz is 10 or 4 10 \text{ or } 4 .

Answer

z=10 or z=4 z = 10 \text{ or } z = 4