Complex Numbers questions
967 published questions with worked solutions.
- If a < 0, b > 0 then a b is equal to
- If n_1, n_2 are positive integers then (1+i)^ n_1 + (1+i^3)^ n_1 + (1+i^5)^ n_2 + (1+i^7)^ n_2 is a real number if and only if
- The complex number 2^ n (1+i)^ 2n + (1+i)^ 2n 2^ n , n Z , is equal to
- The smallest positive integral value of n for which ( 1-i 1+i )^ n is purely imaginary with positive imaginary part, is
- If (a+ib)^5 = + i then (b+ia)^5 is equal to
- If i= -1 , the number of values of i^ n + i^ -n for different n Z is
- Im (z) is equal to
- The value of (1+i)^3 + (1-i)^6 is
- ^ -1 1i(z-1) , where z is nonreal, can be the angle of a triangle if
- If n is an odd integer, i= -1 , then (1+i)^ 6n + (1-i)^ 6n is equal to
- If z_1 = 9y^2 - 4 - 10ix, z_2 = 8y^2 - 20i, where z_1 = z_2, then z = x+iy is equal to
- If z = 1 + i , where < < 3 2 , then |z| is equal to
- If z is a complex number satisfying the relation |z+1| = z + 2(1+i) then z is
- If (1+i)z = (1-i) z then z is
- If z_1, z_2 are two nonzero complex numbers such that |z_1+z_2| = |z_1| + |z_2| then amp z_1 z_2 is equal to
- The complex number z is purely imaginary if
- If z = x+iy such that |z+1| = |z-1| and amp z-1 z+1 = 4 then
- Let z = + i - i , 4 < < 2. Then z is
- If z = 3 + i 3 - i then the fundamental amplitude of z is
- If 1+2i 2+i = r( + i ) then
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