HARD
JEE Main/Advance
IMPORTANT
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The number of common solutions of the equations zn=1+i and zm=2-i,n,mN zC is

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Important Questions on Complex Numbers

HARD
JEE Main/Advance
IMPORTANT
Let ω=cos3°+isin3° then r=110Reω2r-1 equals
EASY
JEE Main/Advance
IMPORTANT
If 1, α1, α2, α3,, α3n are the roots of equation z3n+1=1, nN and ω is an imaginary cube root of unity. Then the value of
α1-ωα2-ωα3-ωα3n-ω is
HARD
JEE Main/Advance
IMPORTANT
If there exist exactly one complex number z satisfying the conditions z-ki3 and arg zπ6 (where kR+ and i=-1), then the value of k is
MEDIUM
JEE Main/Advance
IMPORTANT
If z-1=1 and z0, 2 then the possible value of z-2z is
MEDIUM
JEE Main/Advance
IMPORTANT
The number of values of z satisfying the equations 1+z+z2+z3++z17=0 and 1+z+z2++z11=0 simultaneously is
MEDIUM
JEE Main/Advance
IMPORTANT
If 1+cosθ+isinθsinθ+i1+cosθ4=cosnθ+isinnθ then value of n is
HARD
JEE Main/Advance
IMPORTANT
The value of n=17xn+1xn2 is (where x is a root of x2-x+1=0)
EASY
JEE Main/Advance
IMPORTANT
If the locus of a point z lying on z-3+z-i=k represent an ellipse, then k can be