Complex Numbers questions
967 published questions with worked solutions.
- 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...
- 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
- 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...
- Let the complex number z=x+iy be such that 2z-3i 2z+i is purely imaginary. If x+y^2=0, then y^4+y^2-y is equal to
- Let A= (0,2 ): 1+2i 1-i is purely imaginary . Then the sum of the elements in A is
- If for z= +i , |z+2|=z+4(1+i), then + and are the roots of the equation
- If and are the roots of the equation x^2-x+1=0, then ^ 101 + ^ 107 is equal to
- If and are the roots of the equation x^2-2x+2=0, then the least value of n for which ( )^n=1 is
- Let S= z C- i,2i : z^2+8iz-15 z^2-3iz-2 R . If - 13 11 i S, R- 0 , then 242 ^2 is equal to
- Let =- ^2 and ^3=1 be two real numbers such that ^ 2009 + ^ 2009 =(- )^ 2009 +(- ^2)^ 2009 and =- [ ( ^3 )^ 869 ^2+ ( ^3 )^ 1337...
- Let the circles C₁ : |z| = r and C₂ : |z − 3 − 4i| = 5, z ∈ ℂ, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ moves on C₂...
- Let x and y be real numbers such that 50 ( 2x 1 + 3i - y 1 - 2i ) = 31 + 17i, i = √−1. Then the value of 10(x − 3y) is:
- Let z be a complex number such that |z + 2| = |z − 2| and arg ( z+3 z-i ) = 4. Then |z|² is equal to:
- Let S = z ∈ ℂ : z² + 4z + 16 = 0 . Then _ z S |z+ 3 i|^2 is equal to:
- Let S= z∈ℂ : z²+√6 iz−3=0 . Then _ z S z^8 is equal to:
- Let the set of all values of k∈ℝ such that the equation z( z+2+i)+k(2+3i)=0, z∈ℂ, has at least one solution, be the interval [α,...
- The number of values of z ∈ ℂ, satisfying the equations |z − (4 + 8i)| = √10 and |z − (3 + 5i)| + |z − (5 + 11i)| = 4√5, is:
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