Complex Numbers questions
967 published questions with worked solutions.
- Consider the following two statements: Statement I: For any two non-zero complex numbers z_1, z_2: (|z_1| + |z_2|) | z_1 |z_1| +...
- Let S_1 = z ∈ C : |z| ≤ 5 , S_2 = z C : Im ( z + 1 - 3i 1 - 3i ) 0 and S_3 = z ∈ C : Re(z) ≥ 0 . Then the area of region S_1 ∩...
- If Re ( z-1 2z+i )=1, where z = x + iy, then the point (x, y) lies on a :
- Let be a root of the equation x^2+x+1=0 and the matrix A= 1 3 bmatrix 1&1&1 1& & ^2 1& ^2& ^4 bmatrix , then the matrix A^ 31 is...
- If the equation, x^2+bx+45=0 (b R) has conjugate complex roots and they satisfy |z+1|=2 10 , then -
- Let = -1+i 3 2 . If a=(1+ ) _ k=0 ^ 100 ^ 2k and b= _ k=0 ^ 100 ^ 3k , then a and b are the roots of the quadratic equation :
- The imaginary part of (3+2 -54 )^ 1/2 - (3-2 -54 )^ 1/2 can be :
- If z₁, z₂ are two distinct complex number such that | z_1 - 2z_2 12 - z_1 z_2 | = 2, then
- The value of ( 1+ 2 9 +i 2 9 1+ 2 9 -i 2 9 )^3 is:
- If ( 1+i 1-i )^ m/2 = ( 1+i i-1 )^ n/3 =1, (m, n ∈ N), then the greatest common divisor of the least values of m and n is...
- Let z be a complex number such that |z + 2| = 1 and Im ( z + 1 z + 2 ) = 15. Then the value of |Re( z + 2 )| is:
- The sum of all possible values of θ ∈ [−π, 2π], for which 1 + i 1 - 2i is purely imaginary, is equal to:
- If a and b are real numbers such that (2+ )^4=a+b , where = -1+i 3 2 , then a + b is equal to :
- If the four complex number z, z , z -2Re( z ) and z-2Re(z) represent the vertices of a square of side 4 units in the Argand...
- The region represented by z=x+iy C:|z|-Re(z) 1 is also given by the inequality :
- Let z = x + iy be a non-zero complex number such that z^2=i|z|^2, where i= -1 , then z lies on the :
- Let a_n = i^ (n+1)^2 , where i = -1 and n = 1, 2, 3, Then the value of a_1 + a_3 + a_5 + + a_ 25 is
- The value of sum _ n=1 ^ 13 (i^n + i^ n+1 ), where i = -1 , equals
- If z = x + iy, z^ 1/3 = a - ib and x a - y b = k(a^2 - b^2), then value of k equals
- The smallest positive integer n for which ( 1+i 1-i )^n = 1, is
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