# Troubleshooting: (-i)^4 Calculation Error on TI-36X Pro Calculator

• Calculators
• moouers
In summary, the conversation discusses why a TI-36X Pro calculator returns a "Domain Error" when calculating (-i)^4, while it works fine on a TI-83 Plus. The possibility of the calculator using logs to calculate the value is mentioned, as well as the manual stating that it cannot compute i to a power greater than 3. It is suggested to consult the user manual or the company's website for more information.
moouers
I'm curious if anyone knows why my calculator would return "Domain Error" when calculating (-i)^4 on my TI-36X Pro?

((-i)^2)^2 works just fine on the machine, and (-i)^4 works just fine on my TI-83 Plus.

Any ideas?

moouers said:
I'm curious if anyone knows why my calculator would return "Domain Error" when calculating (-i)^4 on my TI-36X Pro?

((-i)^2)^2 works just fine on the machine, and (-i)^4 works just fine on my TI-83 Plus.

Any ideas?
The only thing I can think of is that the calculator might be using logs to calculate the value. The following is an identity for real x > 0.

xn = (eln(x))4 = e4ln(x).

It's possible that it is programmed to be able to calculate i2 and (-i)2, but for other powers it uses a different algorithm

Consult your user manual - it might have some information about the domains of the functions it can calculate. I'm sur they have a web site, and they might have a site where you can ask questions about the specific models.

Thank you, Mark. I apologize for not recognizing your post sooner! I checked my user manual and it only says that it cannot compute i to a power greater than 3.

## What does (-i)^4 equal to?

The expression (-i)^4 means (-i)(-i)(-i)(-i) which simplifies to 1. This is because when we multiply two complex numbers with the same argument, the result is a real number equal to the product of their magnitudes.

## Why is there a domain error when (-i)^4 is evaluated?

The domain error occurs because the expression (-i)^4 is not defined in the complex number system. When we raise a complex number to a power, we use De Moivre's theorem which only applies to numbers with a non-negative real part. Since (-i) has a negative real part, we cannot use De Moivre's theorem and thus get a domain error.

## Can (-i)^4 be expressed in terms of real numbers?

Yes, (-i)^4 equals to 1 which is a real number. This is because when we raise a complex number to the fourth power, the result is always a real number.

## What is the geometric interpretation of (-i)^4?

The geometric interpretation of (-i)^4 is a rotation of 360 degrees (or 0 degrees) around the origin in the complex plane. This is because when we raise a complex number to the fourth power, we essentially multiply its argument by 4.

## How can we evaluate (-i)^4 without getting a domain error?

To evaluate (-i)^4 without getting a domain error, we can use the polar form of complex numbers. We can rewrite (-i) as 1(cos(270) + isin(270)) and then apply De Moivre's theorem to raise it to the fourth power. This will result in 1(cos(1080) + isin(1080)) which simplifies to 1. Therefore, (-i)^4 equals to 1 without getting a domain error.

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