Complex Numbers questions
967 published questions with worked solutions.
- Find the complex number z satisfying the equations | z-12 z-8i |= 53, | z-4 z-8 |=1
- If 1, , ^2, , ^ n-1 are the n, n^ th roots of unity and z_1 and z_2 are any two complex numbers, then _ r=0 ^ n-1 |z_1+ ^rz_2 |^2=
- If z_n= n(n+1)(n+2) +i n(n+1)(n+2) for n=1,2,3, , then the valu of (z_1z_2 z_n) is
- If |z-25i| 15, then | maximum amp (z)- minimum amp (z)|=
- The area of the triangle formed by the points representing -z, iz and z-iz in the Argand plane is
- If |z-4-3i| 1 and m and n are the least and greatest value of |z| and is the least value of x^4+x^2+4 x in the interval (0, )...
- If is an imaginary cube root of unity, then the value of ( ^ 10 + ^ 23 ) - 4 is
- Let be a complex cube root of unity. If the equation |z- |^2+ |z- ^2 |^2= represents a circle with points representing and ^2 as...
- The system of equation |z+1-i|= 2 and |z|=3 has
- If z+z^ -1 =1, then z^ 100 +z^ -100 is equal to
- (1+i)^8+(1-i)^8=
- If the complex numbers z_1=a+i, z_2=1+ib, z_3=0 form the vertices of equilateral triangle (a,b are real numbers between 0 and 1),...
- The value of expression 2(1+ ) (1+ ^2 )+3(2+ ) (2+ ^2 )+4(3+ ) (3+ ^2 )+ +(n+1)(n+ ) (n+ ^2 ), where is an imaginary cube root of...
- If A,B,C are three points in the Argand plane representing the complex numbers z_1,z_2,z_3 such that z_1= z_2+z_3 +1 , where R,...
- The roots of the cubic equation (z+ )^3= ^3, 0
- The value of [ 2 (56^ 15')+i (56^ 15') ]^8 is
- If z_1,z_2,z_3,z_4 represent the vertices of a rhombus taken in the anticlockwise order, then
- If +i = ^ -1 (z), z=x+iy and is constant, the locus of z' is
- For any complex number z, the minimum value of |z|+|z-2i|, is
- If z is a non-real 7^ th root of -1, then z^ 86 +z^ 175 +z^ 289 is equal to
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