| 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.
Correct Answer: D
Solution :
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 \[({{z}^{2}})=-\frac{\pi }{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
