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|I m(z)||z|^(n-1.)

If z=(i)^(i)^(((i)))w h e r e i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

If z=1/((1-i)(2+3i)), then |z| is (a) . 1 (b ). 1/sqrt(26) (c) . 5/sqrt(26) (d) . none of these

If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqrt(2)+1 c. sqrt(2)-1 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

If A=[costheta-sinthetasinthetacostheta] , then A^T+A=I_2 , if theta=npi,\ \ n in Z (b) theta=(2n+1)pi/2,\ \ n in Z (c) theta=2n\ pi+pi/3,\ \ n in Z (d) none of these

If L_1 is the line of intersection of planes 2x+y+z=1a n d3x+y+2z=2a n dL_2 is line x=y=z , Which option is correct? (a)Shortest distance between L_1a n dL_2i s1/(sqrt(2)) Equation of L_1i s(x-1)/1=(y+1)/(-1)=(z-0)/(-1) (b)Shortest distance between L_1a n dL_2 is sqrt(2) Equation of L_1i s(x-1)/1=(y+1)/(-2)=(z-0)/(-1) (c) None of these

If the point representing the complex number z_alpha is a point on or inside the circle having centre (0+i0) and radius alpha then maximum value of |z_1+z_2+……+z_n|= (A) (n(n+3))/2 (B) (n(n+1))/2 (C) (n(n-1))/2 (D) none of these

If B: {z: |z-3-4i|}=5 and C={z:Re[(3+4i)z]=0} then the number of elements in the set B intesection C is (A) 0 (B) 1 (C) 2 (D) none of these

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these