Help Needed

I have a doubt , please help me out !!

In the given figure , P , Q , R are 3 complex numbers . Angle PQR = $\theta$

How do I represent theta using only the amplitudes of the given complex numbers ?

Also if $Z_1 Z_2 Z_3$ be 3 complex numbers taken in the complex plane in the anticlockwise sense , then how can I represent the angle $Z_1 Z_2 Z_3$ in terms of the individual amplitudes of the complex numbers ?

P.S. The angles/amplitude part of the complex numbers is the only thing that has kept me confused , the other parts ar clear to me . Please help me out !!

#Algebra #ComplexNumbers #HelpMe! #Help #Argument

Easy Math Editor

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

I'm assuming that by amplitudes you mean magnitudes. I don't know if there is an equation exclusively in terms of the magnitudes, but this link discusses the dot product adapted for complex vectors, from which you can determine $\theta.$

Brian Charlesworth - 6 years, 3 months ago

Thanks for the link sir . But I was referring to the angle made by the complex number with the origin sir as in argument of a complex number .

I am not able to understand the concept of arg $\frac{Z_1 - Z_2}{Z_3-Z_2}$ , what does it mean and how to use it in calculations ? This is my doubt sir , please see the pic that I have provided sir ?

Uchiha Robert - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$