Complex Numbers - Geometry

If the complex number z = 3 + 4i represents a point in the Argand plane, what is the modulus of z?

The complex number z = cos 60° + i sin 60° lies on which quadrant of the Argand plane?

If z = 2(cos θ + i sin θ) and w = 3(cos φ + i sin φ), what is the modulus of the product zw?

Given z = 1 + i and w = 1 - i, find the argument of the product zw.

If the points represented by complex numbers z1 and z2 satisfy |z1 - z2| = 0, what can be said about z1 and z2?

The complex number z satisfies |z| = 1 and z + 1/z = 2 cos α. What is the geometric interpretation of this relation?

Find the locus of points z in the Argand plane satisfying |z - 2| = |z + 2|.

If z = x + iy satisfies |z - i| = 1, what is the equation of the locus of z in Cartesian form?

If the complex numbers z1, z2, and z3 represent vertices of an equilateral triangle in the Argand plane, which of the following is true?

If z and w are complex numbers such that |z| = |w| = 1 and arg(z) = θ, arg(w) = φ, what is the area of the triangle formed by points 0, z, and w in the Argand plane?