If `Z` is an idempotent matrix, then `(I+Z)^n` `I+2^n Z` b. `I+(2^n-1)Z` c. `I-(2^n-1)Z` d. none of these

If n is a positive integer, prove that |I m(z^n)|lt=n|Im(z)||z|^(n-1.)

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^-sin^(2x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (n-1/2)pi,n in Z (d) none of these

If a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n z_1+z_2=0 b. z_1z_2=1 c. z_1=z _2 d. none of these

The general solution of cosxcos6x=-1 is x=(2n+1)pi,n in Z x=2npi,n in Z x=npi,n in Z (d) none of these

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- barw z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 z= z (d) None of these

If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= A. (a+i b)/(1+c) B. (b-i c)/(1+a) C. (a+i c)/(1+b) D. none of these

The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i|=3 are a. one b. two c. four d. none of these

If z=x+i y , then he equation |(2z-i)/(z+1)|=m represents a circle, then m can be (a) 1/2 b. 1 c. 2 d. 3

The point z_1=3+sqrt(3)i and z_2=2sqrt(3)+6i are given on la complex plane. The complex number lying on the bisector of the angel formed by the vectors z_1a n dz_2 is a. z=((3+2sqrt(3)))/2+(sqrt(3)+2)/2i b. z=5+5i c. z=-1-i d.none of these