Complex Numbers questions
967 published questions with worked solutions.
- If z = 1 + i , - 2 < < 0 then |z| is equal to
- If z is a nonreal complex number then which of the following may not be real?
- If z = , ^2, where is a nonreal complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane then...
- Let z_1 = r_1e^ i _1 and z_2 = r_2e^ i _2 , where r_1 > 1, r_2 > 1. STATEMENT-1: |1 - z_1z_2| > |z_1 - z_2|. STATEMENT-2: |z_1 -...
- The area of the region in the Argand plane in which z can belong, satisfying the inequalities 1 |z - 1| 4 and z + z 2, is
- If the centroid of an equilateral triangle ABC in the Argand plane be at z = 1, the vertex C is at z = = -1 - 3 i 2 and A, B, C...
- If amp z_1 - z_2 z_1 - z_3 = 2 , where |z_1| |z_2| |z_3|, then the points representing z_1, z_2 and z_3 are
- Let z, be complex numbers such that z + i = 0 and (z ) = . Then z equals
- If |z_1| = |z_2| = 1 and amp z_1 + amp z_2 = 0 then
- If z_1, z_2, z_3 are complex numbers such that |z_1| = |z_2| = |z_3| = | 1 z_1 + 1 z_2 + 1 z_3 | = 1 then |z_1 + z_2 + z_3| is
- If z < 0 then (-z) - z is equal to
- The complex numbers z_1, z_2 and z_3 satisfying z_1 - z_3 z_2 - z_3 = 1 - 3 , i 2 are the vertices of a triangle which is
- Let z_1 and z_2 be nth roots of unity which are ends of a line segment that subtend a right angle at the origin. Then n must be...
- For all complex numbers z_1, z_2 satisfying |z_1| = 12 and |z_2 - 3 - 4i| = 5, the minimum value of |z_1 - z_2| is
- A man walks a distance of 3 units from the origin towards the north-east (N 45° E) direction. From there, he walks a distance of...
- If |z| = 1 and z 1 then all the values of z 1 - z^2 lie on
- A particle P starts from the point z_0 = 1 + 2i, where i = -1 . It moves first horizontally away from origin by 5 units and then...
- Let z_1 and z_2 be two distinct complex numbers and let z = (1-t)z_1 + tz_2 for some real number t, where 0 < t < 1. If (w)...
- Match the statements in **Column I** with those in **Column II**. [**Note:** Here z takes values in the complex plane and Im (z)...
- Let = 2 3 + i 2 3 . Then the number of distinct complex numbers z satisfying vmatrix z + 1 & & ^2 & z + ^2 & 1 ^2 & 1 & z +...
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