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Topic: [HM] Bombelli: Cube root of Complex Nos.
Replies: 8   Last Post: Feb 19, 2001 5:31 AM

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Prof. Dr. Jochen Ziegenbalg

Posts: 31
Registered: 12/3/04
Re: [HM] Bombelli: Cube root of Complex Nos.
Posted: Feb 14, 2001 5:57 PM
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On Wed, 14 Feb 2001, Bonnie Shulman wrote:

> BUT, in actually computing
> the real and imaginary parts of 2 + 11i, I am left evaluating
> cos(arctan 11/2) (or sin of same). Is there a way to compute
> this analytically (series?) so as to get exactly 2 or 1, rather
> than a numerical approximation? [I suspect so, as my calculator
> gives the exact answers.]


Any (hand-held) calculator will hardly be able to give the exact
answer (even if the display seems to say so), nor will be the usual
floating-based programming languages or spreadsheets (due to the
inherent limitations of floating point arithmetic with the usually
implemented constant "word-length"), but using a computer algebra
system usually will do.

Best regards,

Jochen Ziegenbalg, Karlsruhe






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