Complex Numbers questions
967 published questions with worked solutions.
- The area of the triangle whose vertices are i, , , where i= -1 and , are the nonreal cube roots of unity, is
- The nonzero real value of x for which (1+ix)(1+2ix) 1-ix is purely real is
- If z_1= 1 a+i , a 0 and z_2= 1 1+bi , b 0 such that z_1= z_2 then
- If is a complex constant such that z^2+z+ =0 has a real root then
- If amp (z_1z_2)=0 and |z_1|=|z_2|=1 then
- If z is a nonzero complex number then | | z|^2 z z | is equal to
- If is a nonreal cube root of unity then the value of 1 (2- )(2- ^2)+2 (3- )(3- ^2)+ +(n-1)(n- )(n- ^2) is
- The value of ^ -n + ^ -2n , n N and is a nonreal cube root of unity, is
- The value of ^ 4n-1 + ^ 4n-2 + ^ 4n-3 , n N and is a nonreal fourth root of unity, is
- Let x be a nonreal complex number satisfying (x-1)^3+8=0 then x is
- If z= 1+3i 1+i then
- If z is different from i and |z|=1 then z+i z-i is
- If z_1,z_2 are two complex numbers then
- Let z_1,z_2 be two complex numbers represented by points on the circle |z|=1 and |z|=2 respectively then
- ABCD is a square, vertices being taken in the anticlockwise sense. If A represents the complex number z and the intersection of...
- If z_1,z_2,z_3,z_4 are the four complex numbers represented by the vertices of a quadrilateral taken in order such that...
- If z_0,z_1 represent points P, Q on the locus |z-1|=1 and the line segment PQ subtends an angle /2 at the point z=1 then z_1 is...
- If |z_1|=|z_2|=|z_3|=1 and z_1,z_2,z_3 are represented by the vertices of an equilateral triangle then
- If amp z-2 2z+3i =0 and z_0=3+4i then
- If z_1 -z_2 and |z_1+z_2|= | 1 z_1 + 1 z_2 | then
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