Let z be a complex number such that z - i z + 2 i = 1 and z = 5 2 . Then, the value of z + 3 i is

Let z be a complex number such that z-iz+2i=1 and z=52 . Then, the value of z+3i is
  1. 10
  2. 72
  3. 154
  4. 23

Solution

Given, z-i=z+2i

⇒x2+y-12=x2+y+22
⇒-2y+1=4y+4
⇒6y=-3⇒y=-12

From, z=52, we get, 
x2+y2=254⇒x2=244=6⇒z=±6-i2
Hence, z+3i=6+254=494
z+3i=72

Asked in: JEE Main 2020 (09 Jan Shift 1)

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