What is the conjugate of a fraction?

Elise Griffith

Elise Griffith

Answered question

2023-02-15

What is the conjugate of a fraction?

Answer & Explanation

lew3i0

lew3i0

Beginner2023-02-16Added 4 answers

Method 1:
A complex number conjugate is another complex number with the same real part as the original complex number and the same magnitude but opposite sign.
To find the conjugate of a fraction, multiply the numerator and denominator by the complex conjugate of the denominator.
Let z=1x+yi is a fraction, then
Rewrite the complex number as a+ib form
z=1x-yix+yix-yi
z=x-yix2-yi2a+ba-b=a2-b2
z=x-yix2--y2i2=-1
z=x-yix2+y2
The conjugate of z is z¯=x+yix2+y2
Method 2: Conjugate radical function
A radical function is a function that contains a square root.
a+b and a-b are conjugate radical.
To determine the conjugate of a fraction, multiply the numerator and denominator by the denominator's conjugate.
Let c=1x+y is a fraction, then
Rewrite the radical function
c=1x-yx+yx-y
c=x-yx2-y2a+ba-b=a2-b2
c=x-yx-y
The conjugate of the radical function is c¯=x+yx-y.

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