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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18.
Imaginary and Complex Numbers
18.1
Introduction to imaginary numbers
18.2
Complex numbers and complex planes
18.3
Adding and subtracting complex numbers
18.4
Complex conjugates
18.5
Multiplying and dividing complex numbers
18.6
Distance and midpoint of complex numbers
18.7
Angle and absolute value of complex numbers
18.8
Polar form of complex numbers
18.9
Operations on complex numbers in polar form
Grade 12 Math
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