Similarities and differences between the Roman Empire and the "Byzantine Empire" (which considered itself the continuation of the Roman Empire).
Comparing Accrual and Cash Accounting. Created by Sal Khan.
Analyzing charts from New York Times to compare income trends across several countries over a 30 year time period. Created by Sal Khan.
Comparison of the processes of mitosis and meiosis. Mitosis produces two diploid (2n) somatic cells that are genetically identical to each other and the original parent cell, whereas meiosis produces four haploid (n) gametes that are genetically unique from each other and the original parent (germ) cell. Mitosis involves one cell division, whereas meiosis involves two cell divisions.
A comparison of the Eastern and Western fronts in WWI
The Civil War is often considered the most transformative event in US history. But how much did it really change American national identity? In this video, Kim compares the relative significance of the effects of the Civil War on American values.
Sal and World History Fellow Steven Schroeder discuss the fall of empires, from Achaemenid Persia, the Maurya Empire in India, the Han Empire in China, and the Roman Kingdom, Republic, and Empire in the Mediterranean.
Comparing what led to the rise of Achaemenid Persia, Maurya India, Han China, and the Roman Empire.
Seeing how an inhibitor can "compete" for an enzyme with the intended substrate.
This 4-minute video lesson introduces Khan's series on complex numbers.
This single minute video lesson looks at how to add complex numbers.
This 4-minute video lesson give an example of a complex conjugate.
This 5- minute video lesson shows how to divide complex numbers.
This 4-minute video lesson looks at the imaginary roots of negative numbers.
This 6-minute video lesson explains how to multiply complex numbers.
This 2-minute video lesson explains how to subtract complex numbers.
A closer look at the complex exponential term in Euler's Formula. We see that it represents a complex number, a distance of 1 from the origin of the complex plane. Created by Willy McAllister.
When we put time in the exponent of a complex exponential, the complex number it represent rotates in a circle on the complex plane. You can think of it as a spinning number! Created by Willy McAllister.
Complex numbers can be represented three ways on the complex plane: cartesian coordinates, radius and angle, and exponential form. Created by Willy McAllister.
Multiplying a real or complex number by the imaginary unit j corresponds to a rotation by +90 degrees. This is the key feature of j that makes it such a useful number. Created by Willy McAllister.