Question:

If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) is

Show Hint

The modulus of a complex number \( z = a + bi \) is given by \( |z| = \sqrt{a^2 + b^2} \).
Updated On: Mar 7, 2025
  • 225
  • 265
  • \( \sqrt{269} \)
  • 200
  • \( \sqrt{265} \)
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

Step 1: Add \( 12 + 9i \) to \( z = 1 + i \): \[ z + 12 + 9i = 1 + i + 12 + 9i = 13 + 10i \] Step 2: Now, calculate the modulus: \[ |13 + 10i| = \sqrt{13^2 + 10^2} = \sqrt{169 + 100} = \sqrt{269} \] Step 3: Thus, the maximum value is \( \sqrt{269} \).
Was this answer helpful?
0
0