Complex Numbers questions
967 published questions with worked solutions.
- If the locus of Z C, such that Re ( z-1 2z+i ) + Re ( z -1 2 z -i ) = 2, is a circle of radius r and center (a, b), then 15ab r^2...
- Let R and C denote the set of real numbers and complex numbers respectively. The function f:C R defined by f(z)=|z| is
- If Q denotes the set of all rational numbers and f ( p q )= p^2-q^2 for any p q Q with p,q integers, q>0 and (p,q)=1, then...
- If ^ -1 (x+iy)= 12 ^ -1 ( 2x 1+x^2+y^2 )+ i 2 ^ -1 ( 2y 1-x^2-y^2 ), x,y R, then ^ -1 (iy) is
- Statement 1: ( 2 7 )+ ( 4 7 )+ ( 8 7 )=- 12. Statement 2: ( 2 7 )+i ( 2 7 ) is a complex 7th root of unity.
- The number of values of p for which the equation ^3x+1+p^3-3p x=0 (p>0) has a root is ____.
- If x=y 2 3 =z 4 3 , then xy+yz+zx=
- If the complex numbers x+i 2x and x-i 2x are conjugates of each other, then x is equal to
- If the expression x 2 + x 2 -i x 1+2i x 2 is real, then x is equal to
- If z is a complex number such that |z| 2, then the minimum value of |z + 1 2 |:
- A value of θ for which 2 + 3i 1 - 2i is purely imaginary, is :
- Let ω be a complex number such that 2ω + 1 = z where z = -3 . If vmatrix 1 & 1 & 1 1 & - ^2 - 1 & ^2 1 & ^2 & ^7 vmatrix = 3k,...
- If , C are the distinct roots, of the equation x^2 - x + 1 = 0, then ^ 101 + ^ 107 is equal to
- The least positive integer n for which ( 1 + i 3 1 - i 3 )^n = 1, is ?
- If α and β be the roots of the equation x^2 - 2x + 2 = 0, then the least value of n for which ( )^n = 1 is:
- If z = 3 2 + i 2 (i = -1 ), then (1 + iz + z^5 + iz^8)^9 is equal to:
- All the points in the set S = + i - i : R (i = -1 ) lie on a:
- If z and w are two complex numbers such that |zw| = 1 and (z) - (w) = 2 , then:
- The set of all R , for which w = 1 + (1 - 8 )z 1 - z is a purely imaginary number, for all z C satisfying |z| = 1 and Re (z) 1, is
- If |z - 3 + 2i| 4 then the difference between the greatest value and the least value of |z| is -
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