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?
Hello, taurus!
Given: .$\displaystyle w\:=\:2-3i\,\text{ and }\,z\:=\:4+3i$
Find: .$\displaystyle \frac{w+z}{w-z}$
We have: .$\displaystyle \begin{array}{ccccc}w + z &=& (2-3i) + (4+3i) &=& 6 \\ w-z & = & (2-3i) - (4+3i) &=& -2 - 6i\end{array}$
. . Then: . $\displaystyle \frac{w+z}{w-z} \;=\;\frac{6}{-2-6i} \;=\;\frac{6}{-2(1 + 3i)} \;=\;\frac{-3}{1 + 3i} $
Rationalize: . $\displaystyle \frac{-3}{1+3i}\cdot\frac{1-3i}{1-3i} \;=\;\frac{-3(1-3i)}{1 - 9i^2} \;=\;\frac{-3(1-3i)}{10}$
Answer: . $\displaystyle -\frac{3}{10} + \frac{9}{10}i$