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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19.
Imaginary and Complex Numbers
19.1
Introduction to imaginary numbers
19.2
Complex numbers and complex planes
19.3
Adding and subtracting complex numbers
19.4
Complex conjugates
19.5
Multiplying and dividing complex numbers
19.6
Distance and midpoint of complex numbers
19.7
Angle and absolute value of complex numbers
19.8
Polar form of complex numbers
19.9
Operations on complex numbers in polar form
Grade 12 Math
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