Complex conjugates

Complex conjugates

We have seen how conjugates had helped us simplify perplexing problems in the trigonometric identities chapter and the radical functions chapter. What if I tell you that the same principles can also be applied to complex numbers to make our lives better! In this section, we will introduce complex conjugates, as well as how to perform addition and subtraction on them.
Basic Concepts: Adding functions, Subtracting functions
Related Concepts: Imaginary zeros of polynomials

Lessons

  • 1.
    Find the conjugate of
    ■ \blacksquare \; 3+4i3+4i
    ■ \blacksquare \; 4−6i4-\sqrt6i
    ■ \blacksquare \; −10+4i-\sqrt{10}+4i
    ■ \blacksquare \; i−5i-5
  • 2.
    Given that z=5+6i z=5+6i , determine z‾+z‾\overline{z}+\overline{z}
  • 3.
    Given that w=i−14 w=i-14 , determine w‾+w\overline{w}+w
  • 4.
    If z=15+2iz=15+2i , w=28i−7w=28i-7, determine w+z‾w+\overline{z}
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49.
Imaginary and Complex Numbers
49.1
Introduction to imaginary numbers
49.2
Complex numbers and complex planes
49.3
Adding and subtracting complex numbers
49.4
Complex conjugates
49.5
Multiplying and dividing complex numbers
49.6
Distance and midpoint of complex numbers
49.7
Angle and absolute value of complex numbers
49.8
Polar form of complex numbers
49.9
Operations on complex numbers in polar form
ACCUPLACER Test Prep
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