Complex Numbers Basics: JEE Questions & Solutions

If x^2+x+1=0, then the value of (x + 1x)^2 + (x^2 + 1x^2)^2 + (x^3 + 1x^3)^2 + + (x^25 + 1x^25)^2 is:

Let = -1 + i 32 and = -1 - i 32, where i = -1. If (7 - 7 + 9)^20 + (9 + 7 - 7)^20 + (-7 + 9 + 7)^20 + (14 + 7 + 7)^20 = m^10 then the value…

Let S = z C: 4z^2 + z = 0. Then z S |z|^2 is equal to

If z = 32 + i2, then (z^201 - i)^8 is equal to

Let z=(1+i)(1+2i)(1+3i) (1+ni), where i= -1. If |z|^2=44200, then n is equal to

Given below are two statements: Statement I: 25^13+20^13+31^13 is divisible by 7 Statement II: The integral part of (7+4 3)^25 is an odd…

Let z1, z2, z3 be three complex numbers on the circle |z| = 1 with (z1) = - 4, (z2) = 0 and (z3) = 4. If |z1 z2 + z2 z3 + z3 z1|^2 = + 2,…

If and are the roots of the equation 2z^2 - 3z - 2i = 0, where i = -1, then 16 Re ( ^19 + ^19 + ^11 + ^11 ^15 + ^15) Im ( ^19 + ^19 + ^11 +…

The number of real solution(s) of the equation x^2 + 3x + 2 = ( |x - 3|, |x + 2|) is:

Let z C be such that z+3iz-2+i = 2+3i. Then the sum of all possible values of z is

Let the product of 1 = (8 + i) + (7 + 4i) and 2 = (1 + 8i) + (4 + 7i) be + i, where i = -1. Let p and q be the maximum and the minimum…

The remainder when ( (64)^64)^64 is divided by 7 is equal to:

The sum of the squares of the roots of |x - 2|^2 + |x - 2| - 2 = 0 and the squares of the roots of x^2 |x - 3| - 5 = 0, is:

If satisfies x^2 + x + 1 = 0 and (1 +)^7 = A + B + C ^2, where A, B, C 0, then 5(3A - 2B - C) is equal to:

Let the complex numbers and 1 lie on the circles |z - z0| = 2 and |z - z0| = 4 respectively, where z0 = 1 + i. Then, the value of 100| |^2…

If z = 1/(2 - 2i) such that |z + 1| = z + (1 + i), where i is the imaginary unit and, are real numbers, then + is equal to:

Let, be the roots of the equation x^2 - 6x + 3 = 0 such that Im() Im(). Let a, b be integers not divisible by 3 and n be a natural number…

If z = x + iy, xy = 0, satisfies the equation z^2 + iz = 0, then |z|^2 is equal to:

If z is a complex number, then the number of common roots of the equations z^1985 + z^100 + 1 = 0 and z^2 + z + 1 = 0 is:

The number of real solutions of the equation x(x^2 + 3x) + |x-1| + 6|k-2| = 0 is:

Let z1 and z2 be two complex numbers such that z1 + z2 = 5 and z1^3 + z2^3 = 20 + 15i. Then |z1^4 + z2^4| equals:

The number of real solutions of the equation 3 (x^2 + 1x^2) - 2 (x+ 1x), is:

The value of ( 1 + 2 9 + i 2 91 + 2 9 - i 2 9)^3 is:

Let S =: 2 (9^2 -4 + 13) - 2 ( 52 3^2 -4 + 1) = 2. Then the maximum value of for which the equation x^2 - 2 ( S)x + S ( + 1)^2 = 0 has real…

For two non-zero complex numbers z1 and z2, if Re(z1 z2) = 0 and Re(z1 + z2) = 0, then which of the following are possible? Choose the…

Let x = ( 8 3+13)^13 and y = ( 7 2+9)^9. If [t] denotes the greatest integer t, then

50th root of a number x is 12 and 50th root of another number y is 18. Then the remainder obtained on dividing x + y by 25 is.....

Let a, b be two real numbers such that ab < 0. If the complex number 1 + aib + i is of unit modulus and a + ib lies on the circle |z - 1| =…

Let a b be two non-zero real numbers. Then the number of elements in the set X = z C: (a z^2 + b z) = a and (b z^2 + a z) = b is equal to:

For,, Z C and 1, if -1 is the radius of the circle |z - |^2 + |z - |^2 = 2, then | - | is equal to:

If for z = + i, |z + 2| = z + 4(1 + i), then + and are the roots of the equation:

Let the complex number z = x + iy be such that 2z - 3i2z + i is purely imaginary. If x + y^2 = 0, then y^4 + y^2 - y is equal to:

Let S = z = x + iy: 2z - 3i4z + 2i is a real number Then which of the following is NOT correct?

For a C, let: A = z C: Re(a + z) Im( a + z), and B = z C: Re(a + z) < Im( a + z). Among the two statements: (S1): If Re(a), Im(a) 0, then…

Let S = z C - i, 2i: z^2 + 8iz - 15z^2 - 3iz - 2 R. If - 1311i S, R - 0, then 242 ^2 is equal to.

Fractional part of the number 4^202215 is equal to:

Let = z z + k1z + k2iz + (1+i), k1, k2 R. Let Re() = 0 be the circle C of radius 1 in the first quadrant touching the line y = 1 and the…

Let S = z C: z = i(z^2 + Re(z)). Then z S |z|^2 is equal to: