My Math Forum Complex Numbers Question

 Geometry Geometry Math Forum

 June 7th, 2014, 06:17 AM #1 Newbie   Joined: Apr 2012 Posts: 9 Thanks: 0 Complex Numbers Question Hey guys, I never understood and learned the way to solve these kind of questions so I will ask for a bit of help before my final exam. Can you please solve this step by step for me? Thank you in advance! Solve the equation z^3=27i and display the solutions in the complex number plane.
 June 7th, 2014, 06:36 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2552 Math Focus: Mainly analysis and algebra Let $z = re^{i\theta}$ then $$z^3 = r^3e^{3i\theta} = 27e^{2n\pi i} \qquad \Longrightarrow \qquad \begin{cases} r = 3 \\ 3\theta = 2n\pi \\ \end{cases}$$ Thus $$z= 3e^{\frac23 n\pi i}$$ Thanks from lilstef
 June 16th, 2014, 07:27 AM #3 Newbie   Joined: Jun 2014 From: Parys Posts: 1 Thanks: 0 Is my try bad or not? »z^3=27i »z^3=3^3i therefore »z=3i.
 June 16th, 2014, 08:25 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2552 Math Focus: Mainly analysis and algebra You haven't taken the cube-root of $i$. I didn't see the $i$ there in the first place! $$z^3 = r^3e^{3i\theta} = 27e^{\left(2n+\frac{1}{2}\right)\pi i} \qquad \Longrightarrow \qquad \begin{cases} r = 3 \\ 3\theta = \left(4n+1\right)\frac{\pi}{2} \implies \theta = \left(4n+1\right)\frac{\pi}{6}\\ \end{cases}$$ Which gives $$z = 3e^{i \frac{\pi}{6} },3e^{i \frac{5\pi}{6} },3e^{i \frac{9\pi}{6} }$$ Last edited by v8archie; June 16th, 2014 at 08:35 AM.

 Tags complex, numbers, question

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post carl17 Algebra 2 October 26th, 2013 11:55 AM Bula Algebra 1 March 27th, 2013 01:48 PM deadsociety Algebra 2 January 14th, 2013 04:36 PM dylan182 Complex Analysis 4 December 16th, 2010 07:05 AM TsAmE Complex Analysis 11 November 17th, 2010 05:49 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top