• # question_answer Direction: For the following questions, choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. Consider the principal argument of a complex number z is 9. Statement I Principal argument of ${{z}^{2}}$ is $2\theta$. Statement II$\arg \,({{z}^{2}})=2\,\arg \,(z)$. A)  Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. B)  Statement I is true. Statement II is also true and Statement n is not the correct explanation of Statement I. C)  Statement I is true. Statement II is false. D)  Statement I is false. Statement II is true.

Statement I If principal argument of z is $\theta$, then argument of ${{z}^{2}}$ will be $2\theta$ $\therefore$ Principal argument of $z=\pi -\frac{\pi }{4}=\frac{3\pi }{4}$ Argument $({{z}^{2}})=2\times \frac{3\pi }{4}=\frac{3\pi }{2}$ But principal argument $({{z}^{2}})=-\frac{\pi }{2}$