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