A few UNI algebra questions (1 Viewer)

[Ragerunner]

Having a bit of trouble

 

[Xayma]

Hmm if I can remember what I did of complex numbers
I can do 1)
I will use @ for theta

cos4@+i sin4@=(cos@+isin@)⁴
Let cos@=c
sin@=s
(cos@+isin@)⁴=c⁴+4c³is+6c²i²s²+4ci³s³+i⁴s⁴
Since i²=-1
c⁴+4c³is+6c²i²s²+4ci³s³+i⁴s⁴=c⁴-6c²s²+s⁴+4c³is-4cis³

Equating real and imaginary

cos4@=c⁴-6c²s²+s⁴
.:cos4@=cos⁴@-6cos²@sin²@+sin⁴@
Now s²=1-c²
=c⁴-6c²(1-c²)+(1-c²)²
=8c⁴-8c²+1
.:
cos4@=8cos⁴@-8cos²@+1

The second one I will post up as soon as I can type it


cos⁵@=(1/2[e^i@+e^-i@]⁵
=1/2⁵(e^5i@+5e^4i@e^-i@+10e^3i@e^-2i@+10e^2i@e^-3i@+5e^i@e^-4i@+e^-5i@)
=1/2⁵(e^5i@+5e^3i@+10e^i@+10e^-i@+5e^-3i@+e^-5i@)
=(1/16)cos5@+(5/16)cos3@+(10/16)cos@

I hope thats right because I havent touched complex numbers since the start of term 4 last year.

 

[Affinity]

Hmm..... you made a mistake..
cos(4t) = 8[cos(t)]^4 - 8[cos(t)]^2 + 1

 

[Xayma]

Originally posted by Affinity
Hmm..... you made a mistake..
cos(4t) = 8[cos(t)]^4 - 8[cos(t)]^2 + 1

Oh yeah I did that when expanding the c²(1-c²).

There was a semi-disclaimer at the bottom anyway

 

[Ragerunner]

Thanks for the answers....damn I can't remember my bionomial expansion -__-

 

[freaking_out]

Originally posted by Ragerunner
Thanks for the answers....damn I can't remember my bionomial expansion -__-

hehe, and u never knew it in the first place.

 

[Xayma]

Originally posted by Ragerunner
Thanks for the answers....damn I can't remember my bionomial expansion -__-

Neither can I, I havent touched it in class yet, I just use Pascal's