Modulus & Argument: JEE Questions & Solutions

The number of complex numbers z, satisfying |z| = 1 and | z z + zz | = 1, is:

Let O be the origin, the point A be z1 = 3 + 2 2i, the point B z2 be such that 3|z2| = |z1| and (z2) = (z1) + 6. Then:

Let integers a, b [-3,3] be such that a + b 0. Then the number of all possible ordered pairs (a, b), for which | z - az + b | = 1 and…

Among the statements: (S1): The set z C - -i: |z| = 1 and z - iz + i is purely real contains exactly two elements. (S2): The set z C - -1:…

Let r and respectively be the modulus and amplitude of the complex number z = 2 - i (2 5 8). Then, (r,) is equal to:

If denotes the number of solutions of |1 - i|^x = 2^x and = |z| (z), where z = - /4 (1 + i)^4, 1 - i, + i, 1 + i, i = -1, then the distance…

Let z = 1 + i and z1 = 1 + i z z(1-z) + 1z. Then 12 arg(z1) is equal to.

The complex number z = i-1 3 + i 3 is equal to:

Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a right angle in the anticlockwise direction, and w2…

The number of real roots of the equation x|x|-5|x+2|+6=0 is

If the set ( z- z+z z2-3z+5 z): z C, (z)=3 is equal to the interval (, ], then 24( -) is equal to