For z ∈ ℂ if the minimum value of z - 3 2 + z - p 2 i is 5 2 , then a value of p is _______.

Step-by-step solution

Note that z - 3 2 is the distance between the point z and 3 2 , 0 on argand plane. Note that z - p 2 i is the distance between the point z and 0 , p 2 on argand plane. ​​​​​​​ z - 3 2 + z - p 2 i is sum of distance of z from A 3 2 , 0 and B 0 , p 2 For minimising the sum, z should lie on A B and A B should be equal to 5 2 Now, A B 2 = 18 + 2 p 2 ⇒ 18 + 2 p 2 = 5 2 2 ⇒ p 2 = 16 i.e. p = ± 4