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.
Key Insights
 🥳 Complex number subtraction involves subtracting the real parts and imaginary parts separately.
 #️⃣ Visualizing complex number subtraction on an Argand diagram involves 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 Argand diagram, with the tail of the negative of the second complex number positioned at the head of the first complex number.
 🤕 The position of the new head of the vector represents the complex number obtained from the subtraction.
 🥳 Manipulating complex number expressions requires adding the real parts to the real parts and the imaginary parts to the imaginary parts.
 #️⃣ Subtracting a complex number is equivalent to adding the negative of that complex number.
 🐬 The negative of a complex number is obtained by flipping the vector representation over the origin on an Argand diagram.
Transcript
Voiceover:So we've plotted two complex numbers right over here on this argand diagram. And what I want to think about is what if we defined a third complex number, C, as being equal to the complex number, A, minus the complex number, B. What is C going to look like if we were to write it as just a sum of its real and imaginary parts and what would ... Read More
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.