Month: November 2023

What is Adjusted Frequency in a Histogram?

Some time ago we looked into the meaning of histograms, on the way to the concept of the Probability Density Function. A recent question focused on the histogram itself, in a way that will add to that discussion. We’ll learn about frequency density, which was overlooked there, and discover an alternative way to label a …

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.