Exponential form of a Complex number
If z = x + iy then e z = e (x + iy) = e x e iy ? e z = e x {cos y + i sin y} is called the Exponential form of the Complex numbe..
To find the qth roots of a Complex number
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2n p + q )} [2n p + q is the general amplitude..
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2n p + q )} [2n p + q is the general amplitude..Cube roots of unity
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..Polar form of a Complex number
is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the amplitude. The general value of the amplitude is q..
is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the amplitude. The general value of the amplitude is q..Dual Nature of Radiation and Matter Summary
Summary - The phenomenon of interference, diffraction and polarization can be explained by the wave theory of light. But the photo electric effect can be explained only using 'photon theory'. That is using particle nature of light. The experimental study of photoelectric effect ..
Summary (Contd..)
Wave optics is based on wave theory of light put forward by Huygen and modified later by Fresnel. According to the wave theory, light is a form of energy, which travels through a medium in the form of transverse waves. A wavefront is defined as the locus of all the particles of ..
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