# complex numbers?

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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.

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.

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#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.

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.

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(Original post by

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.

**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.

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#4

(Original post by

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.

**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.

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#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.

So yes, he means use DeMoivre's formula.

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#6

(Original post by

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.

**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.

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

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#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 ...

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 ...

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