## Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

# Complex numbers

### #1

Posted 26 February 2014 - 05:26 PM

### #2

Posted 27 February 2014 - 11:06 AM

I can do it with 3 multiplications and 4 additions. Still looking.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 04 March 2014 - 12:17 PM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

Posted 11 March 2014 - 10:02 PM

As nobody found the solution, can you post it?

### #5

Posted 13 March 2014 - 12:48 PM

I = (a+b)(c+d) - R =ac+bc+ad+bd - (ac - bd) ... = ... +2*bd ....

**Edited by harey, 13 March 2014 - 12:50 PM.**

### #6

Posted 13 March 2014 - 04:14 PM

@bonanova - sorry, but I believe you have a sign error with the factor bd:

I = (a+b)(c+d) - R =ac+bc+ad+bd - (ac - bd) ... = ... +2*bd ....

Right. It's (a+b)(c+d) - ac - bd.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #7

Posted 13 March 2014 - 04:46 PM

### #8

Posted 15 March 2014 - 03:27 PM

If our hardware uses fewer clock cycles to perform three additions than a single multiplication, we may well gain overall processing speed by using Eq. (2-4) and Eq. (2-5) instead of Eq. (1-2) for complex multiplication

If it worked, it would be great for fractal pictures. The bad news is that multiplications are in the processor heavily optimized, a fair guess 4-5 additions. Googling:

The latency is 1 cycle for an integer addition and 3 cycles for an integer multiplication. You can find the latencies and thoughput in Appendix C of the "Intel 64 and IA-32 Architectures Optimization Reference Manual", which is located on http://www.intel.com...cessor/manuals/.

The big question is how the 3 temporary variables were treated by the compiler. If we have to access the RAM...

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users