Mathematics questions
18011 published questions with worked solutions.
- The vertices B and D of a parallelogram are 1-2i and 4+2i. If the diagonals are at right angles and AC=2BD, the complex number...
- The locus of the points representing the complex numbers z for which |z|-2=|z-i|-|z+5i|=0 is
- The smallest positive integer n for which ( 1+i 1-i )^n=1 is
- If 2< < 3 2, the modulus and argument form of (1+ 2 )+i 2 is
- If z is a complex number such that z 0 and Re (z)=0, then
- Let z_1,z_2,z_3 be three complex numbers satisfying 1 z_1 + 1 z_2 + 1 z_3 =0. Let z_k=r_k( _k+i _k) and _k= 2 _k+i 2 _k z_k for...
- If z=x+iy and w= 1-iz z-i , then |w|=1 implies that in the complex plane
- If z is a complex number satisfying z+z^ -1 =1, then z^n+z^ -n , n N has the value
- Let 3-i and 2+i be affixes of two points A and B the argand plane and P represents the complex number z=x+iy. Then, the locus of...
- The equation z z+(4-3i)z+(4+3i) z+5=0 represents a circle of radius
- The complex numbers z_1,z_2,z_3,z_4 taken in that order in the Argand plane represent the vertices of a parallelogram iff
- If z 0 be a complex number and (z)= /4, then
- Given that a' is a fixed complex number, and ' is a scalar variable, the point z satisfying z=a(1+i ) traces out
- The value of expression (1+ 1 ) (1+ 1 ^2 )+ (2+ 1 ) (2+ 1 ^2 )+ (3+ 1 ) (3+ 1 ^2 )+ + (n+ 1 ) (n+ 1 ^2 ), where is an imaginary...
- If A+ B+ C=0, A+ B+ C=0 and A+B+C=180^ , then the value of 3A+ 3B+ 3C is
- If 1, , ^2 are the cube roots of unity, then vmatrix 1+ & ^2&- 1+ ^2& &- ^2 ^2+ & &- ^2 vmatrix =
- If a+b+c 0, then (a+b +c ^2)^3+(a+b ^2+c )^3=
- If a= 2i , then which of the following is correct?
- The locus of the point z satisfying ( z-1 z+1 )=k, where k is non-zero real, is
- If |z_1|=|z_2|=|z_3| and z_1+z_2+z_3=0, then z_1,z_2,z_3 are vertices of