Finding the parallel impedance in a circuit

[badaboom]

Homework Statement

I need to find the total impedance in a circuit that has:
j60 ohms, 30 ohms, -j60 ohms and 20 ohms in parallel

Homework Equations

Z_total=1/(Z₁+ Z²+ Z_n)

The Attempt at a Solution

I've tried doing this, but what I think is the -j60 and the j60 should cancel therefore leaving only the 30 ohms and 20 ohms in parallel, which would equal 1/50, but the answer says it is 12 ohms.

Attached is an image of the circuit and answer.

 

[gneill]

Homework Statement

I need to find the total impedance in a circuit that has:
j60 ohms, 30 ohms, -j60 ohms and 20 ohms in parallel

Homework Equations

Z_total=1/(Z₁+ Z²+ Z_n)

The Attempt at a Solution

I've tried doing this, but what I think is the -j60 and the j60 should cancel therefore leaving only the 30 ohms and 20 ohms in parallel, which would equal 1/50, but the answer says it is 12 ohms.

Attached is an image of the circuit and answer.

So then, 1/30 + 1/20 = 1/50 ? Check your math.

 

[haxor489]

Parallel impedance is:

Ztotal=[1/(Z1+ Z2+ Zn)]^-1

Also remember when adding fractions you must have a common denominator.

For example 1/a + 1/b = (a+b)/ab

 

[badaboom]

but how does that j5 get up there?

 

[haxor489]

To be honest i think that's a mistake. The negative and positive j components cancel out. That should say 5/20 not j5/j20 even though those two ratios are equivalent.

If you're having trouble adding fractions try this page:
http://www.webmath.com/addfract.html