**Author** |
**Message** |

**azerbajdzan** Veteran poster
Post Number: 790
| Posted on Sunday, 13 February, 2011 - 07:42 pm: | |
those of you, who do not like tomorrow's Valentine's Day like I do, can spend that day by thinking why I called f(z) the Valentine's Day's function... ;-) [display]f(z)=\frac{(z-6)^2 (z+16)^2 \left(z^2-24 z+180\right) \left(z^2-18 z+277\right) \left(z^2+2 z+197\right) \left(z^2+20 z+136\right)}{(z-5) (z+17) \left(z^2-24 z+244\right) \left(z^2-18 z+85\right) \left(z^2-8 z+272\right) \left(z^2+12 z+136\right) \left(z^2+26 z+173\right)}[/display] On the other hand if you like Valentine's Day and forgot to buy something for your friend/partner then feel free to use this function as a gift ;-) |

**Jewbinson** Veteran poster
Post Number: 453
| Posted on Sunday, 13 February, 2011 - 07:53 pm: | |
Is z complex or real or what? |

**azerbajdzan** Veteran poster
Post Number: 791
| Posted on Sunday, 13 February, 2011 - 08:26 pm: | |
z is real or complex or whatever... but further extensions of complex numbers are beyond me... :-) |

**MathsFan** Prolific poster
Post Number: 255
| Posted on Sunday, 13 February, 2011 - 08:44 pm: | |
I don't understand it... |

**Jewbinson** Veteran poster
Post Number: 454
| Posted on Sunday, 13 February, 2011 - 09:16 pm: | |
It could be anything... |

**azerbajdzan** Veteran poster
Post Number: 792
| Posted on Sunday, 13 February, 2011 - 09:29 pm: | |
stay tuned for tomorrow revelation :-) |

**Sam Cappleman-Lynes** Prolific poster
Post Number: 219
| Posted on Sunday, 13 February, 2011 - 09:46 pm: | |
Plot the roots on an Argand Diagram ;) You should get something nice. |

**Jewbinson** Veteran poster
Post Number: 455
| Posted on Sunday, 13 February, 2011 - 10:10 pm: | |
Ok... so what of the denominator? |

**Sam Cappleman-Lynes** Prolific poster
Post Number: 220
| Posted on Sunday, 13 February, 2011 - 10:14 pm: | |
It's just there for confusion, I guess... |

**azerbajdzan** Veteran poster
Post Number: 794
| Posted on Monday, 14 February, 2011 - 11:41 am: | |
Here is a graph of f(z) isn't it nice? ;-) |

**James Cranch** Veteran poster
Post Number: 1927
| Posted on Monday, 14 February, 2011 - 12:46 pm: | |
**quote:**It's just there for confusion, I guess...
Guess again. |

**azerbajdzan** Veteran poster
Post Number: 795
| Posted on Monday, 14 February, 2011 - 01:27 pm: | |
sometimes ordinary things (such as rational function) may look very different when we look at them from other point of view... first example is view "from the side" and the following is "from above" vertical axis is real and horizontal is imaginary... (they are swapped compared to usual usage letting the shape to be in upright position) ...so that's the shape of my heart :-) just to support the romantic atmosphere here are some nice lyrics... Sting - Shape Of My Heart Sting - Shape Of My Heart 2 not to be completely out of topics of this forum try to think about mathematical explanation why this function looks exactly as it looks... (hue represents argument of f(z), luminance represents absolute value of f(z)) |

**Daniel Fretwell** Veteran poster
Post Number: 1108
| Posted on Monday, 14 February, 2011 - 06:48 pm: | |
I wondered why some of the things in the denominator were 1 more than some of the things in the numerator, now it makes sense. Poles and roots make for nice pictures :p |

**Balakrishnan V** Veteran poster
Post Number: 818
| Posted on Monday, 14 February, 2011 - 11:53 pm: | |
Alternatively |

**elvinc** Veteran poster
Post Number: 466
| Posted on Tuesday, 15 February, 2011 - 10:16 pm: | |
very clever. Well done |

**Steve Hewson** Frequent poster
Post Number: 165
| Posted on Wednesday, 16 February, 2011 - 08:23 am: | |
That is fab! |