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

Explanation:

Multiply numerator and denominator by the conjugate of the denominator.

`(4-3i)/(4+3i)=((4-3i)(4-3i))/((4+3i)(4-3i))=(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.