Assertion (A): If the arguments of barz1 and z2 are (π/5) and (π/3) respectively, then arg (z1 z2) is (2 π/15) Reason (R): For any complex number z, arg barz=(π/2)+ arg z The collect option among the following is

Question

Assertion (A): If the arguments of barz1 and z2 are (π/5) and (π/3) respectively, then arg (z1 z2) is (2 π/15) Reason (R): For any complex number z, arg barz=(π/2)+ arg z The collect option among the following is (A) (A) is true, (R) is true and (R) is the correct explanation for (A) (B) (A) is true, (R) is true but (R) is not the correct explanation for (A) (C) (A) is true but (R) is false (D) (A) is false but (R) is true

Tardigrade Admin · Accepted Answer

We have, arg ( barz1)=(π/5), arg (z2)=(π/3) ∴ arg (z1 z2)= arg (z2)- arg ( barz1)=(π/3)-(π/5)=(2 π/15) Also, arg ( barz)=- arg (z). (A) is ture but (R) is false.

Q. Assertion (A): If the arguments of $\overset{z}{ˉ}_{1}$ and $z_{2}$ are $\frac{π}{5}$ and $\frac{π}{3}$ respectively, then $ar g (z_{1} z_{2})$ is $\frac{2 π}{15}$
Reason (R): For any complex number $z, ar g \overset{z}{ˉ} = \frac{π}{2} + ar g z$
The collect option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A)

(A) is true, (R) is true but (R) is not the correct explanation for (A)

(A) is true but (R) is false

(A) is false but (R) is true

We have, $ar g (\overset{z}{ˉ}_{1}) = \frac{π}{5}, ar g (z_{2}) = \frac{π}{3}$
$∴ ar g (z_{1} z_{2}) = ar g (z_{2}) - ar g (\overset{z}{ˉ}_{1}) = \frac{π}{3} - \frac{π}{5} = \frac{2 π}{15}$
Also, $ar g (\overset{z}{ˉ}) = - ar g (z)$ .
(A) is ture but (R) is false.

Q. Assertion (A): If the arguments of zˉ1​ and z2​ are 5π​ and 3π​ respectively, then arg(z1​z2​) is 152π​ Reason (R): For any complex number z,argzˉ=2π​+argz The collect option among the following is