Complex number| class 11th | L-1 , Complete chapter

The conjugate of a complex number is 1/(i-1) . Then the complex number is

Class 7th ch 1 notes

Let A(z_1) and (z_2) represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as (z_1-z_2)/(bar z_1-bar z_2) .If the line l_1 , with complex slope omega_1, and l_2 , with complex slope omeg_2 , on the complex plane are perpendicular then prove that omega_1+omega_2=0 .

If the conjugate of a complex numbers is 1/(i-1) , where i=sqrt(-1) . Then, the complex number is

If z_(1) and z_(2) are complex numbers of two points, then prove that the complex number of the point, which divides the distance between them internally in the ratio l:m is given by (l z_(2) + mz_(1))/(l+m)

Let z=1+ai be a complex number, a > 0 ,such that z^3 is a real number. Then the sum 1+z+z^2+...+ z^11 is equal to: