If `z=1/((1-i)(2+3i)),` then `|z|` is a. `1` b. `1/sqrt(26)` c. `5/sqrt(26)` d. non 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 |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 z=(1)/((2+3i)^(2)), then |z| is a.(1)/(13) b.(1)/(5) c.(1)/(12)d .non of these

If z=((1+i)/(1-i)), then z^(4) equals a.1b.-1c0d non of these

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to a. sqrt(3) b. 2sqrt(2) c. sqrt(10) d. sqrt(26)

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to a. sqrt(3) b. 2sqrt(2) c. sqrt(10) d. sqrt(26)

If z=i log(2-sqrt3), then a. cosz=-1 b. (-1)/2 c. 1 d. 1/2

If iz^(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

If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. 1 d. 2