`" If "(1+i)^(100)=2^(49)(alpha+i beta)" then "sqrt(alpha^(2)+beta^(2))`

The lengths of the sides of a triangle are alpha-beta,alpha+beta and sqrt(3 alpha^(2)+beta^(2)),(alpha>beta>0) Its largest angle is

If alpha and beta are connected by the relations alpha^(2)+alpha=1 and beta^(2)+beta=1, then the value of alpha^(2)+beta^(2) is eqal to

If alpha and beta the roots of the equation ax^(2)+bx+c=0 then the sum of roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0(i)-(alpha^(2)-beta^(2))(ii)(alpha+beta)^(2)-2 alpha beta(iii)alpha^(2)beta+beta^(2)alpha+2 alpha beta(iv)(alpha^(2)+beta^(2))

If A=[[2,3],[1,4]] and if (A+I)^(-1)=alpha A+beta I then (alpha,beta)= ? (where I is identity matrix and alpha,beta in R

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) then tan(alpha+2 beta)tan(2 alpha+beta)=

If alpha,beta in R are such that 1-2i (here i^(2)=-1 ) is a root of z^(2)+alpha z+beta=0 , then (alpha-beta) is equal to:

If alpha,beta are roots of the equation x^(2)-px+q=0, then find the value of (i)alpha^(2)(alpha^(2)beta^(-1)-beta)+beta^(2)(beta^(2)alpha^(-1)-alpha)

If alpha and beta are roots of the quadratic polynomial f(x)=px^(2)+qx+r ;then find the value of (i) alpha^(2)+beta^(2)( ii) (alpha)/(beta)+(beta)/(alpha) (iii) (1)/(alpha^(3))+(1)/(beta^(3))( iv )(alpha^(2))/(beta)+(beta^(2))/(alpha)

Prove that | alpha+sqrt(alpha^(2)-beta^(2))|+| alpha-sqrt(alpha^(2)-beta^(2))|=| alpha+beta|+| alpha-beta| where alpha,beta are complex numbers.

If sin (alpha + beta)=1, sin (alpha- beta)= (1)/(2) , then tan (alpha + 2beta) tan (2alpha + beta) =