Subtracting complex numbers  Imaginary and complex numbers  Precalculus  Khan Academy  Summary and Q&A
TL;DR
Learn how to subtract complex numbers and visually represent the result on an Argand diagram.
Questions & Answers
Q: How can complex numbers be subtracted?
Complex numbers can be subtracted by subtracting their real parts and imaginary parts separately. For example, to subtract (6 + 2i) from (2  i), we subtract the real parts (2  6 = 4) and the imaginary parts (1  2i = 3i), resulting in the complex number 4  3i.
Q: How can complex number subtraction be visualized on an Argand diagram?
To visualize complex number subtraction on an Argand diagram, first plot the original complex numbers A and B as vectors. Then, add the negative of the second complex number (B) to the first complex number (A). This is equivalent to subtracting B from A. The new head of the resulting vector C represents the complex number obtained from the subtraction.
Q: What does the negative of a complex number look like on an Argand diagram?
The negative of a complex number can be visualized by flipping the complex number vector over the origin. For example, if the complex number B is (2  i), its negative (B) would be (2 + i), and when plotted on the Argand diagram, it would be reflected across the origin.
Q: How can the complex number subtraction be represented on an Argand diagram?
The complex number obtained from subtraction, C, can be represented as a vector on the Argand diagram. The tail of C is positioned at the origin, the tail of B is placed at the head of A, and the resulting vector C extends from the tail of B to a new head, which represents the complex number C.
Summary & Key Takeaways

The video teaches how to subtract complex numbers by determining the difference between their real parts and imaginary parts.

It explains how to visualize complex number subtraction on an Argand diagram by adding the negative of the second complex number to the first complex number.

The resulting complex number can be represented as a vector on the diagram.