# Thread: complex numbers

1. ## complex numbers

z1=4.5e^o.5j
z2=3+j

2. Originally Posted by cheesepie

z1=4.5e^o.5j
z2=3+j
The first thing to do is to convert z1 into a + bj form:
$\displaystyle z_1 = 4.5(cos(0.5) + j sin(0.5)) \approx 3.9491 + 2.1574 \, j$

Now consider:
$\displaystyle \frac{1}{\frac{1}{z_1} + \frac{1}{z_2}}$

$\displaystyle = \frac{1}{\frac{1}{z_1} + \frac{1}{z_2}} \cdot \frac{z_1z_2}{z_1z_2}$

$\displaystyle = \frac{z_1z_2}{\frac{1}{z_1} \cdot (z_1z_2) + \frac{1}{z_2} \cdot (z_1z_2)}$

$\displaystyle = \frac{z_1z_2}{z_2 + z_1}$

So insert your expressions for z1 and z2 into this and there's your answer.

Warning! You will need to rationalize the denominator before you are done!

-Dan

3. $\displaystyle z_1 \,=\,4.5e^{0.5}\qquad z_2\,=\,3+j$
Typo the first should read:

$\displaystyle z_1 =4.5e^{0.5\ \bold{j}}$

RonL