# Complex Numbers



## jdd18vm (Jan 6, 2007)

Sorry if this is a seemingly silly question, it will likely be the first of many.

Given: 3+j5 Volts, 4-j10 Amps need to find Impedance (Z=V/I)

Will a Casio 115MS perform this? If so anyone know the steps? (Manual pretty vague)

I converted this to Polar and still didnt get the answer -.3+j0.43 Ohms

Any help would be wlecome.

J


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## Frontier05 (Jan 6, 2007)

> Sorry if this is a seemingly silly question, it will likely be the first of many.
> Given: 3+j5 Volts, 4-j10 Amps need to find Impedance (Z=V/I)
> 
> Will a Casio 115MS perform this? If so anyone know the steps? (Manual pretty vague)
> ...


I used the HP33s and found the two line view stack to be much easier then the single line view. Beside, I'm so used to rpn anyways.

Apparently that casio will convert polor to rectangular, etc., but you have to toggle between screens since it's a single line view so it takes a little more effort.

Remember to always use polor to multiply and divide and rectangular to add and subtract.

View attachment 255


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## clay1492 (Jan 6, 2007)

The HP 33S and the Casio FX-115MS will both work with complex numbers. I used the HP 33S for the FE (April 06), but a friend told me about the Casio FX-115MS before I started studying for the PE (Passed Oct 06). I decided to buy the Casio just to see how easy it was (only $15 bucks). I quickly realized that the Casio was much easier to use. This is coming from someone that uses the HP 48GX in real life and had just spent three months using the HP 33S to prepare and take the FE. My advice is if you are leaning toward the HP, blow 15 bucks and try out the Casio for a week. I think that you will find that the Casio is a better product to handle complex numbers. In addition, the HP 33S is a crapy calculator. It is difficult to tell the difference between commas and decimals, and the whole calculator is cheap feeling.

Just my opinion. Good luck on the exam.

Clay


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## Art (Jan 6, 2007)

> Sorry if this is a seemingly silly question, it will likely be the first of many.
> Given: 3+j5 Volts, 4-j10 Amps need to find Impedance (Z=V/I)
> 
> Will a Casio 115MS perform this? If so anyone know the steps? (Manual pretty vague)
> ...


imo opinion it's easier to just crunch the numbers

sq rt(3sq + 5sq) arctan 5/3

over

sq rt(4sq + -10sq) arctan -10/4

=

5.83 59 deg/10.77 -68.2 deg

=

.54 127.2 deg

= cos 127.2 .54 + j sin 127.2 .54

= -0.33 + j 0.43


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## grover (Jan 6, 2007)

I never had much luck with trying to use my Casio fX115MS+ to do any complex math. I did use the rect/polar fundtions to convert back and forth all the time though.


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## singlespeed (Jan 6, 2007)

I bought the casio fx115ms for two reasons - complex numbers and simultaneous equations. Worked well for both tasks. It can not do simultaneous equations with complex numbers though.

While I agree with Art that it's no big thing to convert back and forth, solving a system of two simultaneous equations using cramers rule is a lot of conversions back and forth between rectangular and polar coordinates.

To the original question:

Enter complex mode: mode 2

enter the following keystrokes: (3+5i)/(4-10i)=-0.33+j0.43

i is the ENG button; in complex mode, it is simply i (engineering notation not available in complex mode); there is no need to use the multiplication key to multiply 5 times i, just enter 5i

The biggest reason why I like the complex math ability is this

-3+j5=?


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## jdd18vm (Jan 7, 2007)

Thanks for the replies everyone

:claps: Singlespeed, I'm embarassed to admit how much time I spent on that when it was that simple.

I got Syntax Error first inputting -3+j5=, til I put it in () then -3?

J


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## singlespeed (Jan 7, 2007)

Don't be embarassed, the calculator instructions are marginal at best. This is why it's best to use the calculator you intend to use for the exam all through your preparations.

Sorry, what I meant was, what is polar notation for -3 +j5?

The long way:

root(-3^2 + 5^2) = 5.83

tan^-1(5/-3) = -59 deg (and this angle is incorrect!)

Picture the real axis (the horizontal abcissa, positive to the right) and the imaginary axis (the vertical ordinate, positive upwards), the angle formed by -3 and j5 is somewhere in the northwest quadrant. So the correct angle is 121 deg.

So, I like a calculator that converts polar to rectangular automatically and vice versa; _*I don't have to remember change the orientaton of the angle by 180 deg if real part is negative*_. It's just one less thing to distract me from the problem at hand. I made this mistake a few times prior to having a calculator that would do it for me - I would be slogging through a bunch of calculations, trying to get the problem done quickly, and I would forget this important step. 

Keep at it and please trust me when I say that the only stupid question is the one that should be asked, and isn't. You have seen that there are folks here that are willing to help - Art, Grover, clay1492, and Frontier05 to name just a few. :thumbsup:


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## grover (Jan 7, 2007)

> To the original question:Enter complex mode: mode 2
> 
> enter the following keystrokes: (3+5i)/(4-10i)=-0.33+j0.43
> 
> i is the ENG button; in complex mode, it is simply i (engineering notation not available in complex mode); there is no need to use the multiplication key to multiply 5 times i, just enter 5i


AH, and shift= to see the real/imaginary coefficient in complex mode instead of alpha e/f! Damn, I wish I'd have known how to use that when I took the exam. Would have saved SOOO much time 

Maybe I should have read the instruction book instead of saying "aw, it looks straightforward enough" and throwing it out.


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## singlespeed (Jan 7, 2007)

the casio fx115ms is definitely worth $15


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## CiceroKid (Jan 7, 2007)

My HP 9s allows for all four functions: adding, subtracting, dividing, and multiplying complex numbers - and you can insert them into the problem in any mixture of polar or rectangular formats. No need to convert between the two formats.

For example, you solve this problem directly: 10&lt;27deg + 6 + j13 = ?

Whatever calculator(s) you use, make sure one of them can handle all 4-functions in mixed formats.

Kid


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