Johnny185
Badges: 0
Rep:
?
#1
Report Thread starter 7 years ago
#1
can someone please help me with these 3 questions on complex numbers?

1)simplify (express in form a+jb) cos3x+jsin3x/cosx +jsinx

2) if z=2+j/1-j find the real and imaginary parts of the complex number z+1/z

3)if x +y are real solve the equation

jx/1+jy = 3x +j4/x +3y


any advice would be much appreciated.
0
reply
tory88
  • Study Helper
Badges: 18
Rep:
?
#2
Report 7 years ago
#2
For 1) write them in exponential form and then use normal exponential division laws.

For 2) Convert 1/z into a number with a real denominator and then add the real and imaginary parts separately to get a + jb

For 3) Convert the LHS to have a real denominator and equate coefficients

Quote me for any more help.
0
reply
Johnny185
Badges: 0
Rep:
?
#3
Report Thread starter 7 years ago
#3
(Original post by tory88)
For 1) write them in exponential form and then use normal exponential division laws.

For 2) Convert 1/z into a number with a real denominator and then add the real and imaginary parts separately to get a + jb

For 3) Convert the LHS to have a real denominator and equate coefficients

Quote me for any more help.

any chance you could be more detailed? sorry i'm pretty new to complex numbers. for the first one do you mean using De moives formula.
0
reply
tory88
  • Study Helper
Badges: 18
Rep:
?
#4
Report 7 years ago
#4
(Original post by Johnny185)
any chance you could be more detailed? sorry i'm pretty new to complex numbers. for the first one do you mean using De moives formula.
For the first one I mean rewrite it as r*e^(i*theta) where you can find r and theta from drawing out the diagram and using trigonometry/Pythagoras. If you show an attempt it would be easier for me to help.
0
reply
aznkid66
Badges: 1
Rep:
?
#5
Report 7 years ago
#5
DeMoivre's formula does the same thing, since it is derived from Euler's formula that states cis(x)=e^ix
So yes, he means use DeMoivre's formula.
0
reply
ztibor
Badges: 10
Rep:
?
#6
Report 7 years ago
#6
(Original post by Johnny185)
can someone please help me with these 3 questions on complex numbers?

1)simplify (express in form a+jb) cos3x+jsin3x/cosx +jsinx

2) if z=2+j/1-j find the real and imaginary parts of the complex number z+1/z

3)if x +y are real solve the equation

jx/1+jy = 3x +j4/x +3y


any advice would be much appreciated.
for 1)
To express in form a+bj multiply the numerator and denominator by cosx-jsinx
Expand the numerator and use addition rules for cos(A-B) and sin(A-B)

for 2)
z=(2+j)(1+j)/2->1/2+3/2j
z'=1/2-3/2j
1/z=z'/(z*z') ->Re(1/z) and Im(1/z)
then add together the real and imagine part of z and 1/z

for 3)
the form of equation is
Multiply both side by (1+jy)(x+3y) and expand both side
You will get two equations one for the real and one for the imagine part
Solve simultaneously for x and y
0
reply
Paxmas
Badges: 2
Rep:
?
#7
Report 6 years ago
#7
Where would we be without Stroud?

For the last question multiply by the denominator, simplify then expand -: (1+jy)(x+3y)
jx(x+3y)=(3x+j4)(1+jy)
jx^2+j3xy=3x+j3xy+j4+j^24y
jx^2+j3xy=3x+j3xy+j4-4y

Collect in form 0=.....
0=(3x-4y)+j(3xy+4-x^2-3xy)
0=REAL (3x-4y)
0=IMAGINARY(4-x^2)

Solve
If 0 = 4-x^2 then x=srt(-4) or (x+2)(x-2)
And if =2 or -2
y=3x/4 ...
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

Should there be a new university admissions system that ditches predicted grades?

No, I think predicted grades should still be used to make offers (514)
33.62%
Yes, I like the idea of applying to uni after I received my grades (PQA) (634)
41.47%
Yes, I like the idea of receiving offers only after I receive my grades (PQO) (312)
20.41%
I think there is a better option than the ones suggested (let us know in the thread!) (69)
4.51%

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