Complex Numbers questions
967 published questions with worked solutions.
- Nonreal complex numbers z satisfying the equation z^3+2z^2+3z+2=0 are
- For a complex number z, the minimum value of |z|+|z-2| is
- If |z|=1 then 1+z 1+ z is equal to
- If is a nonreal cube root of unity then | ^n|, n Z , is equal to
- Let z_1=a+ib, z_2=p+iq be two unimodular complex numbers such that Im (z_1 z_2)=1. If _1=a+ip, _2=b+iq then
- If |z_1-1|<1, |z_2-2|<2, |z_3-3|<3 then |z_1+z_2+z_3|
- If |z-i| 2 and z_0=5+3i then the maximum value of |iz+z_0| is
- If |z|= |z-1|,|z+1| then
- |z-4|<|z-2| represents the region given by
- | z-1 z+1 |=1 represents
- The roots of the equation 1+z+z^3+z^4=0 are represented by the vertices of
- The angle that the vector representing the complex number 1 ( 3-i)^ 25 makes with the positive direction of the real axis is
- If |z_1|=|z_2|=|z_3|=|z_4| then the points representing z_1,z_2,z_3,z_4 are
- Suppose z_1,z_2,z_3 are the vertices of an equilateral triangle inscribed in the circle |z|=2. If z_1=1+ 3 i and z_1,z_2,z_3 are...
- Suppose z_1,z_2,z_3 are the vertices of an equilateral triangle circumscribing the circle |z|=1. If z_1=1+ 3 i and z_1,z_2,z_3...
- If amp z-1 z+1 = 3 then z represents a point on
- If z is a complex number such that | z-3i z+3i |=1 then z lies on
- Let z_1 and z_2 be two nonreal complex cube roots of unity and |z-z_1|^2+|z-z_2|^2= be the equation of a circle with z_1,z_2 as...
- Let R . If the origin and the nonreal roots of 2z^2+2z+ =0 form the three vertices of an equilateral triangle in the Argand plane...
- Let OP OQ=1 and let O, P, Q be three collinear points. If O and Q represent the complex numbers 0 and z then P represents
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