username42530853
Badges: 8
Rep:
?
#1
Report Thread starter 1 month ago
#1
Given that f(x)=\frac{3x}{1-8x+25x^2} = \frac{3x}{(1-(4+3i)x)(1-(4-3i)x)}, how do we then go to showing that f(x)=\frac{i}{2}(1-5e^{-i\phi}x)^{-1} - \frac{i}{2}(1-5e^{i\phi}x)^{-1}? I get the use of partial fractions but I can't see how you end up with a complex exponential in both terms? Would someone be able to explain?
Last edited by username42530853; 1 month ago
0
reply
mqb2766
Badges: 19
Rep:
?
#2
Report 1 month ago
#2
Not sure what you're confused about but they've simply written
4+3i = 5e^(i*phi)
(or similar) and its complex conjugate for 4-3i. Then use partial fractions as you say.
0
reply
username42530853
Badges: 8
Rep:
?
#3
Report Thread starter 1 month ago
#3
(Original post by mqb2766)
Not sure what you're confused about but they've simply written
4+3i = 5e^(i*phi)
(or similar) and its complex conjugate for 4-3i. Then use partial fractions as you say.
Ah yes of course, thank you
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Feeling behind at school/college? What is the best thing your teachers could to help you catch up?

Extra compulsory independent learning activities (eg, homework tasks) (14)
6.7%
Run extra compulsory lessons or workshops (33)
15.79%
Focus on making the normal lesson time with them as high quality as possible (34)
16.27%
Focus on making the normal learning resources as high quality/accessible as possible (31)
14.83%
Provide extra optional activities, lessons and/or workshops (56)
26.79%
Assess students, decide who needs extra support and focus on these students (41)
19.62%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise