CIE A Level Maths: Pure 3复习笔记8.2.2 Geometry of Complex Addition, Subtraction & Conjugation

What does addition look like on an Argand diagram?

• The addition of complex numbers can be shown by the addition of corresponding column vectors
  • Ifand, then
  • This can be written as

• • An alternative is to write adding the respective real and imaginary parts separately

• A complex numbercan be represented by the position vector

What does subtraction look like on an Argand diagram?

• As with addition we can use knowledge of vectors to represent subtraction of complex numbers
  • If and , then
  • This can be written as
  • 

• • An alternative is to write subtracting the respective real and imaginary parts separately

What are the geometric representations of complex addition and subtraction?

• Let w be a given complex number with real part a and imaginary part b
  • 
• Let z be any complex number represented on an Argand diagram
• Adding w to z results in z being translated by vector
• Subtracting w from z results in z being translated by vector

What is the geometric representation of complex conjugation?

• If we plot complex conjugate pairs on an Argand diagram, we notice the points are reflections of each other in the real axis
• Let z be any complex number represented on an Argand diagram
• Complex conjugating z results in z being reflected in the real axis