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# Absolute value of Complex Number Watch

1. Just taking the absolute value of a complex number, I am struggling to see how my book has gone from:

Z(n)=(n+2i)^4.exp(in^4-n)

to:

*Absolute value Z(n)*=(n^2+4)^2.exp(-n)

I have tried expanding the (n+2i)^4 multiplied by (cosn^4+isin(n^4)) /e^n - where the second term has been obtained using Eulers formula - and then trying to seperate the real and imaginary parts before squaring and sq.rooting etc,but it looks very messy so I think I may be going wrong.

Many thanks for any assistance, greatly appreciated .

2. for real t
3. Yes , I'm okay with the exponential terms now. Its just taking the absolute value of (n+2i)^4, I'm struggling to see how its abolute value is (n^2+4)^2.

Heres my working:
- expanding (n+2i)^4 = n^4-24n^2-32in+8in^3+16
and then taking the absolute value of this by seperatng into real and imaginary parts involves an sqrt(n^8) power and sqrt(n^6) power . So I'm struggling to see how this will reduce too n^4+8n^2+16.

4. (Original post by rainbowsss)
Yes , I'm okay with the exponential terms now. Its just taking the absolute value of (n+2i)^4, I'm struggling to see how its abolute value is (n^2+4)^2.

Heres my working:
- expanding (n+2i)^4 = n^4-24n^2-32in+8in^3+16
and then taking the absolute value of this by seperatng into real and imaginary parts involves an sqrt(n^8) power and sqrt(n^6) power . So I'm struggling to see how this will reduce too n^4+8n^2+16.

Can you see what to do now
5. Ahhh I see. thanks very much !

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Updated: April 5, 2013
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