# Math Help - Complex Number division

1. ## Complex Number division

Given w=2-3i and z=4+3i

How do i calculate:
(w+z)/(w-z)?

I thought addition top line and subtraction bottom line then divide but that did not give the right answer?

2. Hello, taurus!

Given: . $w\:=\:2-3i\,\text{ and }\,z\:=\:4+3i$

Find: . $\frac{w+z}{w-z}$

We have: . $\begin{array}{ccccc}w + z &=& (2-3i) + (4+3i) &=& 6 \\ w-z & = & (2-3i) - (4+3i) &=& -2 - 6i\end{array}$

. . Then: . $\frac{w+z}{w-z} \;=\;\frac{6}{-2-6i} \;=\;\frac{6}{-2(1 + 3i)} \;=\;\frac{-3}{1 + 3i}$

Rationalize: . $\frac{-3}{1+3i}\cdot\frac{1-3i}{1-3i} \;=\;\frac{-3(1-3i)}{1 - 9i^2} \;=\;\frac{-3(1-3i)}{10}$

Answer: . $-\frac{3}{10} + \frac{9}{10}i$

3. How did u get 6, i got 6+1i?

thanks

4. Why did the 1i dissappear?

5. How did you get that? $3i - 3i = 0 \neq i$ There never was an 'i', so how could it have disappeared?