Complex Numbers questions
967 published questions with worked solutions.
- Let n denote the number of solutions of the equation z^2+3 z=0, where z is a complex number. Then the value of _ k=0 ^ 1 n^k is...
- Let i = -1 . If (-1+i 3)^ 21 (1-i)^ 24 + (1+i 3)^ 21 (1+i)24 =k, and n = [|k|] be the greatest integral part of |k|. Then _ j=0 ^...
- If the least and the largest real values of , for which the equation z + |z-1|+2i = 0 (z C and i= -1 ) has a solution, are p and...
- i^2+i^4+i^6+ upto (2k+1) terms, k N is
- The sum of i-2-3i+4 upto 100 terms, where i= -1 is
- Let C be the set of all complex numbers Let S_1= z ||z-3-2i|²=8 , S_2= z |Re(z) 5 and S_3= z ||z- z| 8 . Then the number of...
- Let C be the set of all complex numbers. Let S_1 = z : |z-2| 1 and S_2 = z : z(1-i) + z(1-i) 4 . Then, the maximum value of |z- 5...
- If S= z C: z-i z+2i R , then :
- Let Z_1 and Z_2 be two complex numbers such that arg(Z_1-Z_2) = 4 and Z_1, Z_2 satisfy the equation |Z – 3| = Re(z). Then the...
- If a_r= 2r 9 +i 2r 9 , r = 1, 2, 3 …. i= -1 , then the determinant vmatrix a_1&a_2&a_3 _4&a_5&a_6 _7&a_8&a_9 vmatrix is equal to :
- A point z moves in the complex plane such that ( z-2 z+2 )= 4 , then the minimum value of |z-9 2-2i|^2 is equal to _______.
- If ( 3+i)^ 100 =2^ 99 (p+iq), then p and q are roots of the equation :
- The least positive integer n such that (2i)^n (1-i)^ n-2 , i = -1 is a positive integer, is ___
- The equation ( z-1 z+1 )= 4 represent a circle with
- Let z be those complex numbers which satisfy |z+5| 4 and z(1+i)+ z(1-i) -10, i= -1 . If the maximum value of |z+1|^2 is + 2, then...
- The sum of the 162^ th power of the roots of the equation x^3-2x^2+2x-1=0 is
- Let A = z ℂ : 1 |z − (1 + i)| 2 and B = z A : |z − (1 − i)| = 1 . Then, B :
- Let S = z ℂ : |z − 3| 1 and z(4 + 3i) + z̄(4 − 3i) 24 . If + i is the point in S which is closest to 4i, then 25( + ) is equal to...
- For z C if the minimum value of (|z − 3 2 | + |z − p 2 i|) is 5 2 , then a value of p is _____
- For n N, let S_n = z C : |z − 3 + 2i| = n/4 and T_n = z C : |z − 2 + 3i| = 1/n . Then the number of elements in the set n N : S_n...
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