If Z₁ 0 and Z₂ be two complex numbers such that Z₂ Z₁ is a purely imaginary number, then | 2 Z₁+3 Z₂ 2 Z₁-3 Z₂ | is equal to:

Step-by-step solution

Let z₁=1+i and z₂=1-i z₂ z₁ = 1-i 1+i = (1-i)(1-i) (1+i)(1-i) =-i 2 z₁+3 z₂ 2 z₁-3 z₂ = 2+3 ( z₂ z₁ ) 2-3 ( z₂ z₁ ) = 2-3 i 2+3 i | 2 z₁+3 z₂ 2 z₁-3 z₂ |= | 2-3 i 2+3 i |= | 2-3 i 2+3 i | [ | z₁ z₂ |= |z₁ | |z₂ | ]= 4+9 4+9 =1