Joan Thompson

2022-01-18

How do I find the complex conjugate of $\frac{12}{5i}$?

Timothy Wolff

Expert

To find a conjugate of a complex number we first have to convert it to a form $a+bi$.
To do this here we can multiply both numerator and denominator by i.
$z=\frac{12}{5i}=\frac{12i}{5{i}^{2}}=\frac{12i}{-5}=-\frac{12i}{5}$
Now to calculate the conjugate we just have to change sign of the imaginary part:
$\stackrel{―}{z}=\frac{12i}{5}$

Kindlein6h

Expert

ln $a+bi$ from, this starts off as:
$0+\frac{12}{5i}$
Note $\left[\frac{12}{5i}=\frac{12}{5}\cdot \frac{1}{i}\right]\ne \left[\frac{12i}{5}=\frac{12}{5}i\right]$
$\frac{12}{5i}\cdot \left(\frac{i}{i}\right)=\frac{12i}{5{i}^{2}}=\frac{12i}{-5}$
We currently have:
$a+bi=0+\frac{12i}{-5}$
The conjugate is $a-bi$, thus we get:
$a-bi=0-\frac{12i}{-5}$
$=\frac{12i}{5}=\frac{12}{5}i$

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