Complex Numbers And Quadratic Equations question 212
Question: If $ a=\sqrt{2i} $ then which of the following is correct [Roorkee 1989]
Options:
A) $ a=1+i $
B) $ a=1-i $
C) $ a=-(\sqrt{2})i $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ a=\sqrt{2i}=\sqrt{2}{i^{1/2}}=\sqrt{2}{{( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} )}^{1/2}} $ $ =\sqrt{2}( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} )=\sqrt{2}( \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i )=1+i $ Trick: Check with options.
BETA
