Complex Numbers questions
967 published questions with worked solutions.
- If 2z_1 3z_2 is purely imaginary number, then | z_1-z_2 z_1+z_2 |^4 is equal to
- If for complex numbers z_1 and z_2, (z_1)- (z_2)=0, then |z_1-z_2| is equal to
- If z_1 and z_2 are two complex numbers such that | z_1-z_2 z_1+z_2 |=1, then
- If k>1, |z_1|<k and | k-z_1 z_2 z_1-kz_2 |=1, then
- The modulus of 2i - -2i is
- The least positive integer n for which ( 1+i 1-i )^n= 2 ^ -1 ( 1+x^2 2x ), where x>0, is
- If |z-i|=1 and (z)= , where 0< < 2, then - 2z equals
- The locus of z=i+2 i ( + 4 ) , where is parameter, is
- The number of solutions of the system of equations Re (z^2 )=0; |z|=2 is
- 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
- 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
- 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...
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