complex numbers Describe the usefulness of the conjugate and its effect on other complex numbers

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The conjugate of a complex number can be very useful when you need a real component;e.g. when rationalizing to remove the imaginary part from the denominator of a fraction.

Some useful properties:

If z is a complex number and z* is its conjugate (z* is used in some applied fields, while zbar ( a z with a bar over it) is used in most math texts)

z=a+bi, z*=a-bi where a,b are real numbers and i is the square root of negative 1.

z+z* is real.

(z)(z*) is real.

(z*)*=z. (z1+z2)*=z1*+z2*.





Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial