HARD
JEE Main
IMPORTANT
Earn 100

Number of ordered pairs z,ω of the complex numbers z and ω, satisfying the system of equations, z3+(ω¯)7=0 and z5·ω11=1 is

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Important Questions on Complex Numbers

MEDIUM
JEE Main
IMPORTANT
Let P denote a complex number Z=rcosθ+isinθ on the Argand's plane and Q denote a complex number 2Z2cosθ+π4+isinθ+π4. If O is the origin, then OPQ is
HARD
JEE Main
IMPORTANT
Let A2,0 and Bz are two points on the circle z=2. Mz' is a point on AB. If the point z¯' lies on the median of the triangle OAB, where O is origin, then argz' is
HARD
JEE Main
IMPORTANT
If a variable circle S touches S1:z-z1=r1 internally and S2:z-z2=r2 externally while the curves S1& S2 touch internally to each other. Then the eccentricity of the locus of the centre of the curve S is equal to
MEDIUM
JEE Main
IMPORTANT
The eccentricity of conic represented by z-2+z-2+17 i=19 is e, then 19e2 is equal to
HARD
JEE Main
IMPORTANT
A, B and C are points represented by complex numbers z1,z2 and z3. If the circumcentre of the ΔABC is at the origin and the altitude AD of the triangle meets the circumcircle again at P, then the complex number representing point P is
HARD
JEE Main
IMPORTANT
Let P (z=x+iy) lie on the curve |z|=2 in Argand plane and a point Q representing z+1z moves on an ellipse having length of semi-major and semi-minor axes as a and b respectively. The value of a2-b2 is