How do I find the complex conjugate of 125i?

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=125i=12i5i2=12i−5=−12i5 Now to calculate the conjugate we just have to change sign of the imaginary part: z―=12i5

ln a+bi from, this starts off as: 0+125i Note [125i=125⋅1i]≠[12i5=125i] 125i⋅(ii)=12i5i2=12i−5 We currently have: a+bi=0+12i−5 The conjugate is a−bi, thus we get: a−bi=0−12i−5 =12i5=125i

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=125i=12i5i2=12i−5=−12i5 Now to calculate the conjugate we just have to change sign of the imaginary part: z―=12i5

ln a+bi from, this starts off as: 0+125i Note [125i=125⋅1i]≠[12i5=125i] 125i⋅(ii)=12i5i2=12i−5 We currently have: a+bi=0+12i−5 The conjugate is a−bi, thus we get: a−bi=0−12i−5 =12i5=125i

Question: "How do I find the complex conjugate of..."

Joan Thompson Answered2022-01-18

How do I find the complex conjugate of

\frac{12}{5 i}

Answer & Explanation

Timothy Wolff

Expert

2022-01-19Added 26 answers

To find a conjugate of a complex number we first have to convert it to a form

a + b i

.
To do this here we can multiply both numerator and denominator by i.

z = \frac{12}{5 i} = \frac{12 i}{5 i^{2}} = \frac{12 i}{- 5} = - \frac{12 i}{5}

Now to calculate the conjugate we just have to change sign of the imaginary part:

\overset{―}{z} = \frac{12 i}{5}

Kindlein6h

Expert

2022-01-20Added 27 answers

a + b i

from, this starts off as:

0 + \frac{12}{5 i}

Note

[\frac{12}{5 i} = \frac{12}{5} \cdot \frac{1}{i}] \neq [\frac{12 i}{5} = \frac{12}{5} i]

\frac{12}{5 i} \cdot (\frac{i}{i}) = \frac{12 i}{5 i^{2}} = \frac{12 i}{- 5}

We currently have:

a + b i = 0 + \frac{12 i}{- 5}

The conjugate is

a - b i

, thus we get:

a - b i = 0 - \frac{12 i}{- 5}

= \frac{12 i}{5} = \frac{12}{5} i

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