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.


  • 1.
    Find the conjugate of
       \blacksquare \; 3+4i3+4i
       \blacksquare \; 46i4-\sqrt6i
       \blacksquare \; 10+4i-\sqrt{10}+4i
       \blacksquare \; i5i-5

  • 2.
    Given that z=5+6i z=5+6i , determine z+z\overline{z}+\overline{z}

  • 3.
    Given that w=i14 w=i-14 , determine w+w\overline{w}+w

  • 4.
    If z=15+2iz=15+2i , w=28i7w=28i-7, determine w+zw+\overline{z}