# Resolving complex number equation - electrical engineering

#### mrjoet

##### New member
Hi,

I am following a text book and I've got this far which I know is correct:

$$\displaystyle V_{S1} = V_{s1}e^{\frac{π}{4}j}$$

$$\displaystyle I_{S2} = I_{s2}e^{\frac{-π}{2}j}$$

$$\displaystyle Z_{L1} = 150j$$

$$\displaystyle Z_{C1} = -66.67j$$

$$\displaystyle Z_{R2L2} = 100 + 50j$$

$$\displaystyle Z_{R1C2} = 3.24 - 19.46j$$

$$\displaystyle V_Y = Z_{R2L2} \frac{V_{S1}(Z_{L1} + Z_{C1} + Z_{R1C2}) + I_{S2}Z_{L1}Z_{R1C2}}{Z_{R2L2}(Z_{L1} + Z_{C1} + Z_{R1C2}) + Z_{L1}(Z_{R1C2}+Z_{C1})}$$

This is where I'm stuck, as I need to get from here to:

$$\displaystyle V_Y = 3.5e^{2.3j}$$

Is anyone able to help solve this?

#### skeeter

##### Elite Member
$$\displaystyle V_{S1} = V_{s1} \cdot \frac{\sqrt{2}}{2}(1 + j)$$

$$\displaystyle I_{S2} = I_{s2} \cdot (-j)$$

what are the values of $$\displaystyle V_{s1} \text{ and } I_{s2}$$ ?

(the lower case "s" subscript values vice the capital ones) ...

#### mrjoet

##### New member
Ah yes sorry I forgot to add those:

$$\displaystyle V_{s1} = 7$$

$$\displaystyle I_{s2} = 25$$

#### skeeter

##### Elite Member
I stored all your given values in alphabetical registers on my calculator ... the result is attached as an image. Converting the rectangular form to exponential is not even close to what you want to see.

#### jonah2.0

##### Full Member
Beer soaked query follows.
I stored all your given values in alphabetical registers on my calculator ... the result is attached as an image. Converting the rectangular form to exponential is not even close to what you want to see.

View attachment 26402
What calculator app is that?

#### skeeter

##### Elite Member
Beer soaked query follows.

What calculator app is that?
TI Nspire CAS

#### mrjoet

##### New member
Hi,

Sorry I was going through this again and realised I gave some incorrect information.

$$\displaystyle I_{s2} = 25*10^{-3}$$ or $$\displaystyle I_{s2} = -0.025j$$

Does that make a difference as I still can't get it to work, I come out with $$\displaystyle 3.53e^{-0.88j}$$

Last edited:

#### mrjoet

##### New member
OK I just realised I have the correct result but I need to take $$\displaystyle 3.53e^{π-0.88j} = 3.53e^{2.26j}$$

#### skeeter

##### Elite Member
$$\displaystyle (\pi -0.88)=2.26$$