Home
Class 11
MATHS
If z is any non-zero complex number, pro...

If z is any non-zero complex number, prove that the multiplicative inverse of z is `bar z/(|z|^2)`. Hence express the following numbers in the form x + iy, where x , y `in` R : `(4- sqrt(-9))^(-1)`.

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 z is any non-zero complex number, prove that the multiplicative inverse of z is bar z/(|z|^2) . Hence express the following numbers in the form x + iy, where x , y in R : (-3+2i)/(4-5i) .

If z is any complex number, prove that : |z|^2= |z^2| .

For any complex number z, prove that : -|z| leR_e (z) le |z| .

For any complex number z, prove that : -|z| leI_m (z) le |z| .

For any complex number z, the minimum value of |z|+|z-1| is :

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .

Factorise the following expressions : x^2 y z + x y^2z + x y z^2

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is