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Determining the nature of a complex quotient

Determining the nature of a complex quotient

IB Year 6 | Grade 12

Consider a number given by \(z=\dfrac{3b-i}{b+i}\) where \(b\in\mathbb{R}\).

  1. Find the value of \(b\) if \(z\) is a real number.
  2. Find the value of \(b\), where \(b>0\), if \(z\) is a purely imaginary number.

Solution:

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Answer:(a) \(b=0\) (b) \(b=\dfrac1{\sqrt3}=\dfrac{\sqrt3}{3}\)

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