Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

An answer to a comlex equation I was working on was $$z = \frac{1}{2} + \frac{i}{2}$$ My teacher further developed it to be $$e^{\frac{i\pi}{4}-\frac{1}{2}\ln{2}}$$ And here's what I tried: $$z = \frac{1}{2} + \frac{i}{2} = z = \frac{1}{\sqrt{2}}e^{\frac{i\pi}{4}} = e^{\frac{1}{2}\ln{2}}e^{\frac{i\pi}{4}} = e^{\frac{1}{2}\ln{2}+\frac{i\pi}{4}}$$

I feel this is stupid, but I can't see why we have different answers. Anyone? Thanks!

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

The mistake occurs here: $$\frac{1}{\sqrt{2}}e^{\frac{i\pi}{4}} = e^{\frac{1}{2}\ln{2}}e^{\frac{i\pi}{4}}.$$ In fact, we have $$e^{\frac{1}{2}\ln{2}}=2^{\frac{1}{2}}=\sqrt{2}.$$ Therefore, we should have $$\frac{1}{\sqrt{2}}=(\sqrt{2})^{-1} = e^{-\frac{1}{2}\ln{2}}.$$ Mixing this, your answer matches with your teacher's answer.

share|improve this answer
    
Thanks! That helped –  yotamoo Feb 6 '12 at 9:46
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.