Question

What is the quotient of the complex number 4-3i divided by its conjugate?

Answer 1

9514 1404 393

Answer:

  0.28 -0.95i

Step-by-step explanation:

Multiply numerator and denominator by the conjugate of the denominator.

  $\dfrac{4-3i}{4+3i}=\dfrac{(4-3i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{7-24i}{25}=\boxed{0.28-0.96i}$

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Additional comment

If the original number is A∠β, the ratio is 1∠(2β), the square of the unit vector in the same direction as the original.