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

Question

If Z1 ≠ 0 and Z2 be two complex numbers such that (Z2/Z1) is a purely imaginary number, then |(2Z1+3Z2/2Z1-3Z2)| is equal to: (A) 2 (B) 5 (C) 3 (D) 1

Tardigrade Admin · Accepted Answer

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)) = (2-3i/2+3i) |(2 z1 + 3 z2/2 z1 - 3 z2)| = |(2-3i/2+3i)| = |(2-3i/2+3i)| [∵ |(z1/z2)|= (|z1|/|z2|)] = (√4+9/√4+9) = 1

Q. If Z1​=0 and Z2​ be two complex numbers such that Z1​Z2​​ is a purely imaginary number, then ∣∣​2Z1​−3Z2​2Z1​+3Z2​​∣∣​ is equal to:

2

5

3

1

Q. If $Z_{1} \neq = 0$ and $Z_{2}$ be two complex numbers such that $\frac{Z _{2}}{Z _{1}}$ is a purely imaginary number, then $∣ ∣ \frac{2 Z _{1} + 3 Z _{2}}{2 Z _{1} - 3 Z _{2}} ∣ ∣$ is equal to: