# Worksheet: Loci in the Complex Plane Using the Argument

In this worksheet, we will practice finding the loci of a complex equation in the complex plane defined in terms of the argument.

**Q1: **

A half line is given by , . Write an equation for the half line in the form , where and are constants to be found.

- A
- B
- C
- D
- E

**Q2: **

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q3: **

Consider , , and in the complex plane.

Find the Cartesian equation of the locus of such that .

- A
- B
- C
- D
- E

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

Where does the locus of meet the locus of ?

- AAt
- BAt and
- CThe two loci do not meet.
- DAt and
- EAt

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

Where does the locus of meet the locus of ?

- AAt and
- BAt
- CAt and
- DThe two loci do not meet.
- EAt

**Q4: **

A half line is given by , . Write an equation for the half line in the form , where and are constants to be found.

- A
- B
- C
- D
- E

**Q5: **

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q6: **

Consider and in the complex plane.

Find the Cartesian equation of the locus of such that .

- A
- B
- C
- D
- E

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

Find the point at which the two loci meet.

- AThe two loci do not meet.
- B
- C
- D
- E

**Q7: **

Find the Cartesian equation of the locus of such that .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q8: **

Which of the graphs shown is the correct representation of the locus of that satisfies ?

- A(b)
- B(a)
- C(e)
- D(d)
- E(c)