Month: November 2023

More On Mixing Trig Functions

I’ve had several occasions in face-to-face tutoring lately to refer to a past post on mixing (that is, composition) of trig and inverse trig functions. Several recent questions have touched directly or indirectly on this same general idea and extended it, so I thought I’d post them.

Complex Powers of Complex Numbers

Having looked at issues surrounding powers and roots of complex numbers, including fractional powers, let’s go even further and consider complex powers of complex bases. Things will get a little weird as we work toward \((2+3i)^{3+2i}\)!

Powers of Roots and Roots of Powers

Last time, we looked at two recent questions about combining squares and roots, and implications for the properties of exponents. We didn’t have space for some older questions that we referred to. Here, we will go there.