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Working with the complex conjugate

Working with the complex conjugate

IB Year 6 | Grade 12

A complex number is given by \(z=5-2i\). Find each of the following.

  1. \(z^*\)
  2. \(zz^*\)
  3. \(z+z^*\) and \(z-z^*\)
  4. \(\dfrac{1}{z}\) in Cartesian form

Solution:

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Answer:(a) \(5+2i\) (b) \(29\) (c) \(10,\ -4i\) (d) \(\dfrac5{29}+\dfrac2{29}i\)

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