Home
Class 11
MATHS
If z= x + iy, x, y real, prove that : |x...

If z= x + iy, x, y real, prove that : `|x|+|y| le sqrt2 |z|`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

Similar Questions

Explore conceptually related problems

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1

If z = x + iy and w=(1-iz)/(z-i) , show that : |w|=1 implies z is purely real.

If tan^-1x + tan^-1y + tan^-1z = pi , then prove that: x + y + z = xyz.

If tan^-1 x + tan^-1y - tan^-1z = 0 , then prove that x + y + xyz = z.

If sin^-1x + sin^-1y + sin^-1z = pi , prove that xsqrt(1-x^2)+y sqrt(1-y^2) + z sqrt(1-z^2) = 2xyz

If x+iy=(a+ib)/(a-ib) , then prove that x^2+y^2=1

Let x,y,z be the vector, such that |x|=|y|=|z| =sqrt(2) and x,y,z make angles of 60^(@) with each other. If x times (y times z) = a , y xx (z xx x)=b and (x xx y) = c The value of y is:

If xy + yz + zx = 1 , prove that : x/(1-x^2)+y/(1-y^2)+z/(1-z^2)= (4xyz)/((1-x^2)(1-y^2)(1-z^2)) .

If x +y+ z=xyz , prove that : (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)= (2x)/(1-x^2). (2y)/ (1-y^2). (2z)/(1-z^2) .