What Is the Locus of Points Z in These Complex Number Equations?

[gaborfk]

Homework Statement

Describe the locus of points z satisfying the given equation.

Homework Equations

Im(2iz)=7
|z-i|=Re(z)

The Attempt at a Solution

I started on the second one:
I think that Re(z) is just x, then
I squared both sides, simplified and got

(y-1)^2=0 is this correct? If so how would I go about the Im(2iz) LHS on the first equation?

Thank you

 

[AlephZero]

(y-1)^2=0 is this correct?

That's the right way to start, but you are not quite done yet.

When you squared the equation, you found the solutions of

|z-i| = +Re(z) or |z-i| = -Re(z).

Draw a picture of your solution (y-1)^2 = 0 on an Argand diagram to see what part of it corresponds to |z-i| = +Re(z)

how would I go about the Im(2iz) LHS on the first equation?

Let z = x + iy, then work out what is the imaginary part of (2iz).

 

[HallsofIvy]

Homework Statement

Describe the locus of points z satisfying the given equation.

Homework Equations

Im(2iz)=7
|z-i|=Re(z)

The Attempt at a Solution

I started on the second one:
I think that Re(z) is just x, then
I squared both sides, simplified and got

(y-1)^2=0 is this correct?

And if (y-1)²= 0, what can you say about y?

If so how would I go about the Im(2iz) LHS on the first equation?

Thank you

Pretty much the same thing. Let z= x+iy. What is 2iz in terms of x and y? What is Im(2iz)?