Mathematics

LIKE TO JOIN ON FACEBOOK ( click here ) Standard results in Complex number (Argand Plane) 1. Section Formula :- 2.  Centroid:- centroid,   3. Equation of a Straight line :- a) Parametric Form:- From triangle OBP or,  b)    or  =>   or   is Purely Real  ........................ (i) And, therefore condition of collinearity of  because if    are collinear then area form by these points must be 0. General Equation of a Straight Line: Where 'a' is a complex number and 'b' is a Purely Real Number. a - complex number, b - Purely Real Number Proof:- From (i) we have , multiply  by 'i' on both sides, Suppose,    and  and   ( since,   ) And,     = b (let) (We know that,   =  Purely Real ) therefore,   = Purely Real (  'b' ) then equation becomes , Where 'a' is a complex number and 'b' is a Purely Real Number. 4. Condition for the four points to be

LIKE TO JOIN ON FACEBOOK ( click here ) De-Moiver's Theorem:- if   then, CASE 1st:  If n is an integer then, CASE 2nd: If n is a rational number ( different from integers) i.e. n = p/q where p,q belong to integers,   and p,q have no common divisor then  has q distinct values and one of these is equal to  . Steps of root finding of a complex number 'z' : Step 1: Convert 'z' into the 'Polar form' where   is the Principal value of the arg.z. i.e.  Step 2: Generalise  , i.e.   , k belongs to integers  Step 3: The nth roots are given by, , where k = 0,1,2,3..........,n - 1 or,  Ques: Find the 4th roos of   ? Sol:   Step 1: Convert   into polar form. if z = x + iy and we want to convert it into polar form then we have to multiply and divide the sum of square of x and y. therefore,  or,  Step 2: Generalize the  therefore,  Step 3: The 4th roots are g