Concept of Rotation – As multiplying a complex number by $e^{i\alpha}$ Let $Z = r.e^{i\theta}$ is a non zero complex number where $r=\vert Z \vert $ and $\theta = arg(Z)$. $\therefore$ when we multiply $e^{i\alpha}$ to Z we get a complex number Say $W=Ze^{i\alpha}=r.e^{i(\alpha + \theta)}$ $\therefore$ Geometrically $Z.e^{i\alpha} = W$ can be obtained by […]

Read MorePermutation and combination :: Distribution of distinct objects into group having variable group size and fixed group size.

Read MoreWhat is a parabola Parabola is a conic section defined as, Locus of a point which moves such that its distance from a fixed point is always in a constant ratio to its perpendicular distance from a fixed line, is called a conic section. $$\frac{PS}{PM}=e\,\,\,\,\,(Constant)$$ where ‘e’ is called as eccentricity of conic section , […]

Read MoreThe solution of by-quadratic equation of degree 4 , such that in the product of two of linear factor and other linear factor , Coefficient of x square and x will remains same

Read MoreEquation of tangent to parabola Equation of tangent to parabola $ y^2\,=\,4ax $ ant any parametric coordinate p(t)=$p(\,at^2,\,2at)$ where t is a parameter and $t\,\in R $ is given by $ yt\,=\,x\,+\,at^2 $ . Hence 1/t is the slope of tangent at point P(t). Let m=1/t Hence equation of tangent will be $\frac{y}{m}\,=\,x\,+\,\frac{a}{m^2} $ i.e […]

Read MoreDistribution of ‘n’ identical objects into ‘m’ numbers of distinct groups. PODCAST ON DISTRIBUTION OF OBJECTS INTO GROUPS Let us consider distribution of n identical objects to m numbers of distinct groups. let $\,x_i \,$ is the number of identical object objects in $i^{th}\, $ group. Therefore $x_1\,+\,x_2\,+\,x_3……….\,+\,x_m\,=\,n\,\,\, ;\,\,\, where\,\, 0\leq x_i\leq n \,,\,\,\, \forall […]

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