Question

Assertion :If arg$\left(z_1{z}_2\right)=2\pi$, then both $z_1$ and $z_2$ are purely real ($z_1$ and $z_2$ have principal arguments). Reason: Principal argument of complex number lies in $(-\pi ,\pi )$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Principle argument lies in the range i.e $(-\pi ,\pi ]$ but not $(-\pi ,\pi )$ only

So reason is wrong.

$Arg(z_1,z_2)=Arg{z}_1+Arg{z}_2$

$=2\pi$

Only possible is ${Arg(z}_1)={Arg(z}_2)=\pi$

So $z_{1}and{z}_2$ are real purely.

So $A$ is true $R$ is false.