1. module question

http://i34.tinypic.com/juakhy.jpg

i know that the module of a complex number is the square root
of the real and complex coefficients

but here i cant see that they done it that way
?

2. Originally Posted by transgalactic
http://i34.tinypic.com/juakhy.jpg

i know that the module of a complex number is the square root
of the real and complex coefficients

but here i cant see that they done it that way
?
It is important to note what $\displaystyle |z - i|^2$ and $\displaystyle |z + i|^2$ represent.

The represent circles in the complex plane. You are trying to find where the circles overlap.

I would convert it to real and imaginary parts...

Let $\displaystyle z = x + iy$.

Therefore

$\displaystyle |z - i|^2 = |z + i|^2$

$\displaystyle |x + iy - i|^2 = |x + iy + i|^2$

$\displaystyle |x + i(y - 1)|^2 = |x + i(y + 1)|^2$

$\displaystyle x^2 + (y - 1)^2 = x^2 + (y + 1)^2$

$\displaystyle (y - 1)^2 = (y + 1)^2$

$\displaystyle y^2 - 2y + 1 = y^2 + 2y + 1$

$\displaystyle -2y = 2y$

$\displaystyle 0 = 4y$

$\displaystyle y = 0$.

So it is telling you that the two circles will overlap on the x-axis.

3. wow you got the correct answer in another way

thanks

4. Originally Posted by transgalactic
http://i34.tinypic.com/juakhy.jpg

i know that the module of a complex number is the square root
of the real and complex coefficients
The modulus of a complex number is the square root of the sum of the squares of the real and complex coefficients.

but here i cant see that they done it that way
?