A) 1
B) \[\sqrt{2}\]
C) \[2\sqrt{2}\]
D) 4
E) 8
Correct Answer: B
Solution :
Given, \[{{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z\] Let\[\sqrt{5}=r\cos \theta ,\sqrt{3}=r\sin \theta \] \[\therefore \] \[{{r}^{2}}=5+3\] \[\Rightarrow \] \[r=2\sqrt{2}\] \[\therefore \] \[{{(r\cos \theta +ir\sin \theta )}^{33}}={{2}^{49}}z\] \[\Rightarrow \] \[|{{r}^{33}}(cos33\theta +i\sin 33\theta )=|{{2}^{49}}z|\] \[\Rightarrow \] \[{{(2\sqrt{2})}^{33}}|\cos 33\theta +i\sin 33\theta |={{2}^{49}}|z|\] \[\Rightarrow \] \[{{2}^{\frac{99}{2}}}(1)={{2}^{49}}|z|\] \[\Rightarrow \] \[|z|={{2}^{\frac{99}{2}-49}}\] \[\Rightarrow \] \[|z|=\sqrt{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
