How do you divide complex numbers?
An example of an AI chatbot conversation about dividing complex numbers.
Can you explain how to divide complex numbers?
Sure! To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator.
What is the conjugate of a complex number?
The conjugate of a complex number a + bi is a - bi, where a and b are real numbers.
Can you show me an example of dividing two complex numbers?
Of course! For example, to divide (3 + 2i) by (1 - 4i), multiply by the conjugate (1 + 4i). The result is (3 + 2i)(1 + 4i) / (1 - 4i)(1 + 4i).
What do I get after simplifying that?
After simplification, you get (11 + 14i) / 17, which can be expressed as approximately 0.65 + 0.82i.
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