After a thorough search, I have found nothing called El pi. Perhaps the person asking the question means what is Pi? In that case, it is a mathematical constant calculated by the ratio of a circle's circumference to its diameter. It is equal approximately to the value 3.14159.
by euler: i=ei(pi)/2 therifore ii = (ei(pi)/2)i=ei^2(pi)/2=e-(pi)/2 ~0.208
No. Say your matrix is called A, then a number e is an eigenvalue of A exactly when A-eI is singular, where I is the identity matrix of the same dimensions as A. A-eI is singular exactly when (A-eI)T is singular, but (A-eI)T=AT-(eI)T =AT-eI. Therefore we can conclude that e is an eigenvalue of A exactly when it is an eigenvalue of AT.
[pi^(1/3)]^2 * pi = pi^(2/3) * pi = pi^(5/3) The answer is the cubic root of pi to the fifth power.
(pi + pi + pi) = 3 pi = roughly 9.4248 (rounded) Well, if you use the common shortened version of pi which is 3.14 and add that 3 times, you get 9.42.
(cos(pi x) + sin(pi y) )^8 = 44 differentiate both sides with respect to x 8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0 cos(pi y) dy/dx - pi sin(pi x) = 0 cos(pi y) dy/dx = sin(pi x) dy/dx = sin (pi x) / cos(pi y)
by euler: i=ei(pi)/2 therifore ii = (ei(pi)/2)i=ei^2(pi)/2=e-(pi)/2 ~0.208
pi you bi ei
The Euler's formula in mathematics states that e^(iฯ) + 1 = 0, where e is the base of the natural logarithm, i is the imaginary unit, ฯ is pi, and 0 is the additive identity. This formula connects exponential functions, complex numbers, and trigonometry in a profound way.
Nobody can prove it because it is not true. It is a real number, though. eix = cos(x) + i*sin(x) Therefore ei*pi/2 = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = i Raising both sides to the ith power, (ei*pi/2)i = ii So that ii = ei*i*pi/2 = e-pi/2 = 0.2079. Gelfond proved that the above value is irrational [transcendental, actually].
When doing roots of imaginary or complex numbers, it's best to work in polar form.A little background first.A complex number is represented by a magnitude and an angle. This comes from Euler's Formula (see related link): eiΘ = cos(Θ) + i sin(Θ) {Θ is in radians}. Note that both eiΘ and [cos(Θ) + i sin(Θ)] have a magnitude of 1, so multiply by the magnitude: AeiΘ = Acos(Θ) + Ai sin(Θ).Now if you have a number [a + bi], the angle Θ = arctan(b/a), but this will give Θ between -pi/2 and pi/2 (-90° & +90°). So to get the other angles, you need to figure what quadrant the complex number is in. If a is positive, then it is left of the imaginary axis and your angle is fine. If a is negative, then you need to add 180° (pi radians) to the angle. Or you can subtract pi radians as well. This works because the 180° turn is on the same line with the same slope, just pointing in the opposite direction. To get the magnitude A, just do sqrt(a2 + b2). Now this is for general complex numbers. The question asked for imaginary numbers, which a = 0, and Θ will be pi/2 for positive imaginaries (b>0) or -pi/2 for b
Ei-501,ei 502,ei 503, ei 504 ,ei 505
: ; Euler's identity http://en.wikipedia.org/wiki/Leonhard_Euler some pretty hardcore math, but is important in alot of different ways.
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