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 Subject: "Real or complex number" Previous Topic | Next Topic
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bitrak
Member since Jul-14-05
Jul-17-05, 02:03 PM (EST)     "Real or complex number"

 What's i^i=? ; i=sqrt(-1)

Subject     Author     Message Date     ID Real or complex number bitrak Jul-17-05 TOP RE: Real or complex number alexb Jul-17-05 1 RE: Real or complex number bitrak Jul-17-05 2 RE: Real or complex number alexb Jul-17-05 3 RE: Real or complex number JJ Jul-18-05 4 RE: Real or complex number bitrak Jul-18-05 5 RE: Real or complex number alexb Jul-18-05 6 RE: Real or complex number kfom Jul-06-06 7 RE: Real or complex number JJ Jul-07-06 8 RE: Real or complex number g Jul-08-06 9 RE: Real or complex number JJ Jul-09-06 10 RE: Real or complex number JJ Jul-09-06 11

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alexb
Charter Member
1858 posts
Jul-17-05, 02:05 PM (EST)    1. "RE: Real or complex number"
In response to message #0

 >What's i^i=? ; Just in a second, but first please tell us what do you mean by>i=sqrt(-1) What does sqrt(-1) mean in your view? bitrak
Member since Jul-14-05
Jul-17-05, 03:38 PM (EST)     2. "RE: Real or complex number"
In response to message #1

 Let i^2=-1 .Calculate i^i=? alexb
Charter Member
1858 posts
Jul-17-05, 03:40 PM (EST)    3. "RE: Real or complex number"
In response to message #2

 Please have a look at https://www.cut-the-knot.org/do_you_know/complex.shtml JJ guest
Jul-18-05, 07:13 AM (EST)

4. "RE: Real or complex number"
In response to message #3

 i = exp(i*pi/2)i^i = exp(i*(i*pi/2)) = exp(-pi/2) bitrak
Member since Jul-14-05
Jul-18-05, 11:38 AM (EST)     5. "RE: Real or complex number"
In response to message #4

 JJ you want to say that i^i have one real solution? alexb
Charter Member
1858 posts
Jul-18-05, 11:42 AM (EST)    6. "RE: Real or complex number"
In response to message #5

 >JJ you want to say that i^i have one real solution? This question I can't answer. However, do please check the link I gave earlier. There is a good discussion of this issue.

kfom guest
Jul-06-06, 08:19 PM (EST)

7. "RE: Real or complex number"
In response to message #0

 I know this sounds really bizarre... I read some book a long time ago, something like "The Story of sqrt(-1)" anyway, all I can remember is the first digit:i^i = 0.2... It's real!It's mindblowing! JJ guest
Jul-07-06, 07:34 AM (EST)

8. "RE: Real or complex number"
In response to message #7

 This isn't surprising at all. Operations and/or functions involving complex numbers often leads to real number. For example, the most simplest cases are :i*i = -1i^i = exp(-pi/2)ln(i)=pi/2cos(i)=cosh(1)cosh(i)=cos(1) g guest
Jul-08-06, 11:08 PM (EST)

9. "RE: Real or complex number"
In response to message #8

 how would you start to compute i^i? t seemes so vague... JJ guest
Jul-09-06, 05:47 AM (EST)

10. "RE: Real or complex number"
In response to message #9

 First : computation of real and imaginary parts of the logarithm of a complex numberln(a+i.b)=x+i.y hence a+i.b = exp(x+i.y) = exp(x).exp(i.y) = exp(x).(cos(y)+i.sin(y))a = exp(x).cos(y) and b = exp(x).sin(y)a^2 + b^2 = exp(2x) and b/a = tan(y)x = (1/2)ln(a^2 +b^2)y = atan(b/a)Case of a=0, b=1 : x=0 and y=pi/2hence : ln(i) = i.pi/2.Second : computation of i^i c^p = exp(p.ln(c)) hence i^i = exp(i.ln(i))ln(i)=i.pi/2 hence i^i = exp(i.(i.pi/2)) i^i = exp((i^2)pi/2) = exp((-1)pi/2)i^i = exp(-pi/2)

JJ guest
Jul-09-06, 05:47 AM (EST)

11. "RE: Real or complex number"
In response to message #0

 Why the signs "plus" aren't correctly transmited in the equations ?

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