# Complex Numbers Geometry

1. Homework Statement
Describe the locus of points z satisfying the given equation.

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

3. 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

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AlephZero
Homework Helper
(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).

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HallsofIvy
Homework Helper
1. Homework Statement
Describe the locus of points z satisfying the given equation.

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

3. 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)?