Solve.
|z-8|=4
The solution is z = 12 or z = 4.
To solve the equation |z-8| = 4, we need to consider two cases, one when z - 8 is positive and the other when it is negative.
Case 1: (z - 8) ≥ 0
If z - 8 is positive, then the absolute value sign does not change anything. So we can write the equation as follows:
z - 8 = 4
To isolate z, we add 8 to both sides of the equation:
z = 4 + 8
z = 12
Case 2: (z - 8) < 0
If z - 8 is negative, then the absolute value sign changes the sign. So we can write the equation as follows:
-(z - 8) = 4
To isolate z, we distribute the negative sign to the expression inside the parentheses:
-z + 8 = 4
Next, we subtract 8 from both sides of the equation to isolate z:
-z = 4 - 8
-z = -4
Multiply both sides of the equation by -1 to solve for z:
z = -(-4)
z = 4
Therefore, the equation |z-8| = 4 has two solutions: z = 12 and z = 4.
To solve the equation |z - 8| = 4, we can split it into two cases: positive and negative.
Case 1: z - 8 = 4
Adding 8 to both sides of the equation, we get:
z = 12
Case 2: -(z - 8) = 4
By distributing the negative sign, we have:
-z + 8 = 4
Subtracting 8 from both sides of the equation, we get:
-z = -4
Multiplying both sides of the equation by -1 to isolate z, we have:
z = 4
Therefore, the two solutions to the equation |z - 8| = 4 are z = 12 and z = 4.