The value of `e^(- pi i)`
a) 1
b) -1
c) i
d) - i

If f(x)=(e^x)/(1+e^x), I_1=int_(f(-a))^(f(a))xg(x(1-x)dx and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx , then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1

sum_(i=1)^20 [(.^20C_(i-1))/(.^20C_i+.^20C_(i-1))]^3=k/21 then find the value of k. (a) 400 (b) 100 (c) 50 (d) 200

If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(-i C),e^(-i B)],[e^(-i C),e^(2i B),e^(-i A)],[e^(-i B),e^(-i A),e^(2i C)]| is (a) 1 (b) -1 (c) -2 (d) -4

The amplitude of 1/i is equal to 0 b. pi/2 c. -pi/2 d. pi

5.The value of (i^(4x+1)-i^(4x-1))/(2) is equal to (a) 1 (b) -1 (c) -i (d) 0

If sinx+cosy=1 and cos2x-cos2y=1 then the values of x and y are (A) x=npi+(-1)^n pi/3, n in I, y=mpi+-pi/6, m in I (B) x=npi+(-1)^n pi/6, n in I, y=mpi+-pi/3, m in I (C) x=npi+(-1)^n pi/4, n in I, y=mpi+-pi/4, m in I (D) none of these

The least positive value of n if ((1 + i)/(1 - i))^(n) = 1 , is (a)1 (b)5 (c)4 (d)6

The value of int_0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -1

The value of (1+i)(1+i^2)(1+i^3)(1+i^4) is a. 2 b. 0 c. 1 d. i

The argument of (1-i)/(1+i) is a. -pi/2 b. pi/2 c. (3pi)/2 d. (5pi)/2