If (5z2/11z1) is purely imaginary, then the value of |(2z1+3z2/2z1-3z2)| is

Question

If (5z2/11z1) is purely imaginary, then the value of |(2z1+3z2/2z1-3z2)| is (A) (37/33) (B) 2 (C) 1 (D) 3

Tardigrade Admin · Accepted Answer

Let (5z2/11z1)=ki, where k is any real constant or (z2/z1)=k' i [where k' =(11/5) k] ...(i) ∴ |(2z1+3z2/2z1-3z2)| =|(z1(2+(3z2/z1))/z1(2-(3z2)z1))| =|(2+3k' i/2-3k' i)| =1

Q. If $\frac{5 z _{2}}{11 z _{1}}$ is purely imaginary, then the value of $∣ ∣ \frac{2 z _{1} + 3 z _{2}}{2 z _{1} - 3 z _{2}} ∣ ∣$ is

$\frac{37}{33}$

$2$

$1$

$3$

Q. If 11z1​5z2​​ is purely imaginary, then the value of ∣∣​2z1​−3z2​2z1​+3z2​​∣∣​ is

3337​

2

1

3

Let 11z1​5z2​​=ki, where k is any real constant or z1​z2​​=k′i [where k′=511​k]...(i) ∴∣∣​2z1​−3z2​2z1​+3z2​​∣∣​ =∣∣​z1​(2−z1​3z2​​)z1​(2+z1​3z2​​)​∣∣​ =∣∣​2−3k′i2+3k′i​∣∣​ =1

Q. If $\frac{5 z _{2}}{11 z _{1}}$ is purely imaginary, then the value of $∣ ∣ \frac{2 z _{1} + 3 z _{2}}{2 z _{1} - 3 z _{2}} ∣ ∣$ is

$\frac{37}{33}$

$2$

$1$

$3$