QJEEM20Mad1d6: JEE Main 2020 Mathematics - Class 11 JEEM20Mad1d6 Solution: Let z be complex number such that

Question

Verified Solution • 2025–26 Session moderate

Let z be complex number such that

| \frac{z - i}{z + 2 i} | = 1

and |z| =

\frac{5}{2}

.
Then the value of |z + 3i| is :

Accepted Answer

Given

| \frac{z - i}{z + 2 i} | = 1

|z – i| = |z + 2i|

(let z = x + iy)

\Rightarrow

x² + (y – 1)² = x² + (y + 2)²

\Rightarrow

y =

- \frac{1}{2}

Also given |z| =

\frac{5}{2}

\Rightarrow

x² + y² =

\frac{25}{4}

\Rightarrow

x² = 6

∴

z =

\pm \sqrt{6}

-

- \frac{1}{2} i

|z + 3i| =

\sqrt{6 + \frac{25}{4}}

=

\frac{7}{2}

Step-by-Step Verified Solution