# Distance between two complex numbers

1. Jun 27, 2004

### naav

Hi...i was wondering if someone could confirm if what i have below is correct...thanks...sorry i can't present a diagram...

z(1) = x + iy and z(2) = x(2) + iy(2) are represented by the vectors OP and OQ on an argand diagram...(O is the origin)...imagine the argand diagram...the upper left hand quadrant...(OQ has an argument of say 30 degrees and OP has an argument of 45 degrees - these pieces of information are not relevant anyway)...

is the following correct...

vector OP + vector PQ = vector OQ...

then vector PQ = vector OQ - vector OP

then vector PQ = |z(2) - z(1)|...

1. was wondering if my notation and understanding here is correct...i used algebra in the second line so i was wondering if that is legit...???...

2. is it correct to say in the last line the vector = the magnitude
...

2. Jun 27, 2004

### AKG

That's fine.
That's wrong. You should have:

$$\vec{PQ} = z_2 - z_1$$

$$|\vec{PQ}| = |z_2 - z_1|$$

Or, in plain text:

vector PQ = z(2) - z(1)
|vector PQ| = |z(2) - z(1)|

3. Jun 28, 2004

### naav

Hi...thank you very much...

i said in my earlier post...

and it was said that it should be...

1. isn't that the same thing...

that vector PQ = the magnitude of [z(2) - z(1)]...???...

4. Jun 28, 2004

### HallsofIvy

No, it is not the same thing: |vector PQ| is a number (the length of the vector PQ), not a vector.

Likewise "vector PQ" is a vector while "the magnitude of [z(2)-z(1)]" is a number.

5. Jun 28, 2004

### naav

thank you very much...