What is locus of Z?

What is locus of Z?

The locus of a point 𝑧 is the set of all the points 𝑧 which satisfy a particular condition. Recall that the modulus represents the distance of a point from the origin.

How do you find a locus?

Here is a step-by-step procedure for finding plane loci: Step 1: If possible, choose a coordinate system that will make computations and equations as simple as possible. Step 2: Write the given conditions in a mathematical form involving the coordinates x and y. Step 3: Simplify the resulting equations.

What is modulus complex numbers?

The absolute value of a complex number , a+bi (also called the modulus ) is defined as the distance between the origin (0,0) and the point (a,b) in the complex plane. | a+bi |=√a2+b2. Example: | −2+3i |=√(−2)2+32 =√4+9 =√13.

What is arg in complex numbers?

In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as. in Figure 1.

What is locus Class 11?

A locus is a set of points, in geometry, which satisfies a given condition or situation for a shape or a figure. The plural of the locus is loci. The area of the loci is called the region. The word locus is derived from the word location.

What is a locus in geometry?

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point is a circle, and the set of points in three-space equidistant from a given point is a sphere.

How do you find the locus of a complex number?

Find the locus of the complex number z = x + iy , satisfying relations (z – 1) = pi4 and |z – 2 – 3i| = 2 . Illustrate the locus on the Argand plane.

How do you find the equation for the complex numbers z?

The complex numbers u and v satisfy the equation: + 2v = 2i and iu + v = 3 Solve the equation for u and v, giving both answer in the form x + iy, where x and y are real. On an Argand diagram, sketch the locus representing complex numbers z satisfying zi1and the locus 3

What is the locus of a parallel line?

So the locus is the parallel line starting at but not including , going into the first quadrant at a angle. Let’s see if we can see it analytically. Let be real and positive.