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:
$z_1 = 4.5(cos(0.5) + j sin(0.5)) \approx 3.9491 + 2.1574 \, j$

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

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

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

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

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

-Dan

3. $z_1 \,=\,4.5e^{0.5}\qquad z_2\,=\,3+j$
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