froggy777
contestada

I will give u brainliest if u actually help me explain this in ur own words :,(

When a complex number is in the denominator, why is it necessary to multiply by the conjugate?

Respuesta :

madethisfortwitch1

Answer:

It just makes doing things (like adding and subtracting other numbers) easier if the denominator is a real number. Other than that we just do it out of tradition

This step is done to make the denominator go from a complex number in the form a+bi into a purely real number in the form a^2+b^2 (where 'a' and b are any real numbers).

This is because multiplying a+bi with its conjugate a-bi leads to the following steps

(a+bi)(a-bi)

(a)^2 - (bi)^2 ... difference of squares

a^2 - b^2*i^2

a^2 - b^2*(-1) .... recall that i^2 = -1

a^2 + b^2

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So for example, if your denominator was 2+3i, then you'd multiply that by the conjugate 2-3i and you'd end up with the final denominator of 2^2+3^2 = 4+9 = 13. In this case, a = 2 and b = 3.

Note: make sure to multiply both top and bottom by a-bi (not just the denominator).

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