• Support PF! Buy your school textbooks, materials and every day products Here!

Complex Arithmetic - Mathematica agrees with me, textbook says I'm wrong.

  • Thread starter jdinatale
  • Start date
  • #1
155
0
mathematica.png





Mathematica agrees with my second solution (not the first one though). The back of my textbook says: "[itex]\sqrt[4]{8}[\cos(\frac{5\pi}{8}) + i\sin(\frac{5\pi}{8})][/itex] and [itex]\sqrt[4]{8}[\cos(\frac{13\pi}{8}) + i\sin(\frac{13\pi}{8})][/itex]"


Edit: The second z in my picture should be |z|, the modulus.

Edit2: Here are the results from mathematica, confirming that both the textbook AND I are right...

http://www.wolframalpha.com/input/?i=(1+-+i)^(3/2)+=+(8^(1/4))[cos(45pi/8)+++i+sin(45pi/8)]
http://www.wolframalpha.com/input/?i=(1+-+i)^(3/2)+=+[8^(1/4)][cos(+13pi/8)+++isin(13pi/8)]

My question is, how did my textbook get that answer?
 

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,619
1,253
You can get rid of multiples of ##2\pi##. For example, you have
$$\frac{21\pi}{8} = \frac{(16+5)\pi}{8} = 2\pi + \frac{5\pi}{8},$$ so your first answer is equivalent to the book's first answer. Similarly, you can show your second answer also matches the book's second answer.
 

Related Threads on Complex Arithmetic - Mathematica agrees with me, textbook says I'm wrong.

Replies
24
Views
804
  • Last Post
Replies
7
Views
978
Replies
0
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
6
Views
1K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
10
Views
1K
Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
2
Views
1K
Top