Solve for z. |z - 1/3| = 4 a. z = 13/3 or z = 11/3 b. z = -13/3 or z = -11/3 c. z = 13/3 or z = -13/3 d. z = 13/3 or z = -11/3

Choice D
z = 13/3 or z = -11/3



Work Shown:

|z - 1/3| = 4
z - 1/3 = 4 or z - 1/3 = -4
using the rule that if |z| = k, then z = k or z = -k for some positive number k

Solve z - 1/3 = 4 to get...
z - 1/3 = 4
z - 1/3+1/3 = 4+1/3
z = 4+1/3
z = 12/3+1/3
z = (12+1)/3
z = 13/3

Solve z - 1/3 = -4 to get...
z - 1/3 = -4
z - 1/3+1/3 = -4+1/3
z = -4+1/3
z = -12/3+1/3
z = (-12+1)/3
z = -11/3

Hope i can you!