On the Argand plane point ' A ' denotes a complex number z 1. A triangle OBQ is made directily similiar to the triangle OAM, where OM =1 as shown in the figure. If the point B denotes the complex number z2, then the complex number corresponding to the point ' Q ' is

Question

On the Argand plane point ' A ' denotes a complex number z 1. A triangle OBQ is made directily similiar to the triangle OAM, where OM =1 as shown in the figure. If the point B denotes the complex number z2, then the complex number corresponding to the point ' Q ' is (A) z 1 z 2 (B) (z1/z2) (C) (z2/z1) (D) (z1+z2/z2)

Tardigrade Admin · Accepted Answer

(z2/|z2|)=(z/|z|) ei θ.....(1) (z1/|z1|)=1 ei θ....(2) substitute the value of e i θ from (2) in (1) ( z /| z |)=( z 2/| z 2|) ⋅ (| z 1|/ z 1) ⇒ ( z /| z |)=( z 2 / z 1/| z 2 / z 1|) ; z =( z 2/ z 1)

Q. On the Argand plane point ' $A$ ' denotes a complex number $z_{1}$ . A triangle $OBQ$ is made directily similiar to the triangle $O A M$ , where $OM = 1$ as shown in the figure. If the point $B$ denotes the complex number $z_{2}$ , then the complex number corresponding to the point ' $Q$ ' is

$z_{1} z_{2}$

$\frac{z _{1}}{z _{2}}$

$\frac{z _{2}}{z _{1}}$

$\frac{z _{1} + z _{2}}{z _{2}}$

Q. On the Argand plane point ' A ' denotes a complex number z1​. A triangle OBQ is made directily similiar to the triangle OAM, where OM=1 as shown in the figure. If the point B denotes the complex number z2​, then the complex number corresponding to the point ' Q ' is

z1​z2​

z2​z1​​

z1​z2​​

z2​z1​+z2​​

∣z2​∣z2​​=∣z∣z​eiθ.....(1) ∣z1​∣z1​​=1eiθ....(2) substitute the value of eiθ from (2) in (1) ∣z∣z​=∣z2​∣z2​​⋅z1​∣z1​∣​⇒∣z∣z​=∣z2​/z1​∣z2​/z1​​;z=z1​z2​​

Q. On the Argand plane point ' $A$ ' denotes a complex number $z_{1}$ . A triangle $OBQ$ is made directily similiar to the triangle $O A M$ , where $OM = 1$ as shown in the figure. If the point $B$ denotes the complex number $z_{2}$ , then the complex number corresponding to the point ' $Q$ ' is

$z_{1} z_{2}$

$\frac{z _{1}}{z _{2}}$

$\frac{z _{2}}{z _{1}}$

$\frac{z _{1} + z _{2}}{z _{2}}$