We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
114
3
avatar

what is \(\sqrt(2) ^ {(\frac{7\pi i}{4})}\) as a complex number?

 Apr 23, 2019
 #1
avatar+5778 
+1

\(\text{do you mean}\\ \sqrt{2^{i7\pi/4}}\)

.
 Apr 23, 2019
 #2
avatar
0

nope

Guest Apr 24, 2019
 #3
avatar+103678 
+1

\(y=(\sqrt2)^{(\frac{7\pi i}{4})}\\ y=2^{(\frac{7\pi }{8}i)}\\ log y=log 2^{(\frac{7\pi }{8}i)}\\ ln y=(\frac{7\pi }{8}i) ln 2\\ e^{ln y}=e^{(\frac{7ln 2\pi }{8}i) }\\ y=e^{(\frac{7(ln 2)\pi }{8})i }\\ y=cos(\frac{7(ln 2)\pi }{8})+isin(\frac{7(ln 2)\pi }{8})\)

 

 

You had better check that very carefully.

 Apr 24, 2019

39 Online Users

avatar
avatar