how to get 2.8 + j3.5 m^(-1) from square root in first line?

[sasuki]

can any one help with this equation ASAP PLZ

\(\displaystyle =\, \sqrt{\strut \left[20\, +\, j\,(6\, \times\, 10^8)\,(0.4\, \times \,10^{-6})\right]\, \left[80\, \times \,10^{-3}\, +\, j\,(6\, \times \,10^8)\,(40\, \times \,10^{-12})\right]\,}\)

\(\displaystyle =\, 2.8\, +\, j\,3.5\, m^{-1}\, =\, \alpha\, +\, j\beta\)

how we get the second line from the first line and what M to the power of -1 symbol means

thanks in advance

 

[Deleted member 4993]

can any one help with this equation ASAP PLZ

\(\displaystyle =\, \sqrt{\strut \left[20\, +\, j\,(6\, \times\, 10^8)\,(0.4\, \times \,10^{-6})\right]\, \left[80\, \times \,10^{-3}\, +\, j\,(6\, \times \,10^8)\,(40\, \times \,10^{-12})\right]\,}\)

\(\displaystyle =\, 2.8\, +\, j\,3.5\, m^{-1}\, =\, \alpha\, +\, j\beta\)

how we get the second line from the first line and what M to the power of -1 symbol means

thanks in advance :grin:

What is the context of this equation - i.e. - what subject matter gave rise to this equation?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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[sasuki]

hello Subhotosh Khan & Denis and any mathematician whom interested thanks for your effort
now it seems that I didn't explain a lot about the topic and what it is about so the topic is about electromagnetic wave and this is the complete slide

here Ive tried to explain in detail the step to solve the equation off course until the part which I don't understand
and i hope one of you super mathematician will figure out how to solve it

:roll::roll::roll::roll::roll:

 

[Deleted member 4993]

can any one help with this equation ASAP PLZ

\(\displaystyle =\, \sqrt{\strut \left[20\, +\, j\,(6\, \times\, 10^8)\,(0.4\, \times \,10^{-6})\right]\, \left[80\, \times \,10^{-3}\, +\, j\,(6\, \times \,10^8)\,(40\, \times \,10^{-12})\right]\,}\)

\(\displaystyle =\, 2.8\, +\, j\,3.5\, m^{-1}\, =\, \alpha\, +\, j\beta\)

how we get the second line from the first line and what M to the power of -1 symbol means

thanks in advance

Let

A = 6*10^8

B = 4 * 10^(-9)

then we have under radical sign:

[20 + j * A * B * 10^2] * [80 * 10^(-3) + j * A * B * 10^(-2)]

= 1.6 + 20ABE-2 j + 8AB j - (AB)^2

= -4.16 + 8.2*2.4 j

=-4.16 + 19.68

Now convert this to \(\displaystyle e^{i\theta}\) format and use DeMoivre's theorem to calculate the square root.

[ Denis, I am in the corner...]

 

[sasuki]

guys guys i love the since of the computation that you have & I admire your effort while you competing and showing muscle to each other :grin: there is someone who is not a mathematician and his knowledge about math is just as each course he take require waiting for a magic formula produce from a great mathematician like you just the formula