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.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 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.
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.
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.
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.
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.