Practice questions
88551 published questions with worked solutions.
- If z and w are non-zero complex numbers such that |zw|=1, (z)- (w)= 2 and zw=a+ib, then find a^2+b^2.
- If and are the roots of the equation ix^2-x+12i=0, then find + .
- The complex equation of straight line L is (4+3i)z+(4-3i) z=24. Find the area of the triangle formed by L, real and the imaginary...
- If |z-25i| 15 and | . (z)- . (z)| is m ^ -1 pq, then find mp-q. (Given that G.C.D. (p,q)=1)
- If is a complex cube root of unity, then find the value of ( a+b +c ^2 c+a +b ^2 + a+b +c ^2 b+c +a ^2 )^2.
- If _ 3 |z|^2-|z|+1 2+|z| 2, then find the least value of |z|.
- Find the least value of k for which |z-2 3i|=k intersects the curve z= 6.
- If |z+4|^2-|z-4|^2=8, then find Re (z).
- Find the sum of all possible values of Im (z) where | z-12 z-8i |= 53 and | z-4 z-8 |=1.
- Find the digital sum of the value of 1(2- ) (2- ^2 )+2(3- ) (3- ^2 )+ +9(10- ) (10- ^2 ), where is a complex cube root of unity.
- If 2 2z=( 3-1)+i( 3+1), then find Re (z^6 ).
- Let |z| 1. If m and n represent max. |z-3| and min. |z-3| respectively, then find m^2-n^2.
- If -7-24i =x+iy, then find x^2+y^2.
- ABCD is a rhombus such that its diagonals AC and BD intersect at point M and satisfy BD=2AC. If points D and M represent the...
- If x+iy= 1 1+ +i , then find 4x^2.
- Let p,q R and (1- 3i )^ 200 =2^ 199 (p+iq), i= -1 . Then p+q+q^2 and p-q+q^2 are roots of the equation
- Let , , be the three roots of the equation x^3+bx+c=0. If =1=- , then b^3+2c^3-3 ^3-6 ^3-8 ^3 is equal to
- The sum of all the roots of the equation |x^2-8x+15 |-2x+7=0 is
- The number of real roots of the equation x|x|-5|x+2|+6=0, is
- For a C, let A= z C: Re (a+ z)> Im ( a+z) and B= z C: Re (a+ z)< Im ( a+z) . The among the two statements: (S1): If Re (a), Im...