June 16th, 2019, 09:42 AM  #1 
Senior Member Joined: Aug 2018 From: România Posts: 112 Thanks: 7  A calculation
Hello all, Calculate $\displaystyle [\cos{(x^2)}+i\sin{(x^2)}]^x$. All the best, Integrator 
June 16th, 2019, 11:14 AM  #2 
Senior Member Joined: Oct 2018 From: USA Posts: 102 Thanks: 77 Math Focus: Algebraic Geometry 
$\displaystyle e^{i \theta} = \cos{(\theta)} + i \sin{(\theta)} $

June 16th, 2019, 01:52 PM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,345 Thanks: 985 Math Focus: Wibbly wobbly timeywimey stuff.  
June 16th, 2019, 02:00 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,646 Thanks: 1476 
$\cos(x^2)+i \sin(x^2) = e^{i x^2}$ $\left(e^{i x^2}\right)^x = e^{i x^3}$ 
June 16th, 2019, 03:18 PM  #5 
Senior Member Joined: Oct 2009 Posts: 911 Thanks: 354  
June 16th, 2019, 05:38 PM  #6 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,345 Thanks: 985 Math Focus: Wibbly wobbly timeywimey stuff.  
June 16th, 2019, 07:36 PM  #7 
Senior Member Joined: Sep 2015 From: USA Posts: 2,646 Thanks: 1476  
June 16th, 2019, 09:42 PM  #8  
Senior Member Joined: Aug 2018 From: România Posts: 112 Thanks: 7  Quote:
I do not understand!I think that $\displaystyle \left(e^{i x^2}\right)^{x} =e^{i^x\cdot x^{2x}}$ where $\displaystyle x\in \mathbb R , x>0$ is an identity and so $\displaystyle \left(e^{i x^2}\right)^{x} = e^{i x^3}$ is an equation.  How do we calculate $\displaystyle [\cos(x^2)+i \sin(x^2)]^x$? All the best, Integrator  

Tags 
calculation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
What is this calculation used for?  MMath  Elementary Math  3  July 7th, 2016 10:13 PM 
Integral calculation based on coordinates / Area under Curve calculation  joskevermeulen  Calculus  1  December 29th, 2015 06:02 AM 
A calculation  Dacu  Elementary Math  9  November 21st, 2014 05:34 PM 
I need help with this calculation  diegosened  Algebra  2  April 7th, 2010 05:53 AM 
How can I do the calculation here  rsoy  Calculus  1  December 31st, 1969 04:00 PM 