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# further maths complex numbers quick question! +rep watch

1. the real and imaginary parts of the complex number z = x + iy satisfy the equation (2-i)x - (1 + 3i)y - 7 =0

a) find the value of x and y
b) find the values of i) modulus of z ii) argz

how would i go about starting this question?

will rep - i'm just really confuddled

jb
2. (Original post by jumblebumble)
the real and imaginary parts of the complex number z = x + iy satisfy the equation (2-i)x - (1 + 3i)y - 7 =0

a) find the value of x and y
b) find the values of i) modulus of z ii) argz

how would i go about starting this question?

will rep - i'm just really confuddled

jb
Equate for real and imaginary numbers.

So to start you off:
z=x+iy so x=real and y=imaginary

2x-y=x (1)
-x-3=y (2)

so simplify:

y=x (1)
y=-x-3 (2)

so sub y into (2) and y=-y-3 therefore y=-1.5 etc...
3. (Original post by JTeighty)
Equate for real and imaginary numbers.

So to start you off:
z=x+iy so x=real and y=imaginary

2x-y=x (1)
-x-3=y (2)

so simplify:

y=x (1)
y=-x-3 (2)

so sub y into (2) and y=-y-3 therefore y=-1.5 etc...
the answers are x=3 and y=-1? :/
but thankyou anyway. jb
4. JTeighty's method is right, it's just that he's written the equations down wrong.

2x-y-7=0

-3-3y=0

And solve as simultaneous equations.

(Expanding out, Re(0) and Im(0))

(Also, is the second part ok?)
5. (Original post by Scallym)
JTeighty's method is right, it's just that he's written the equations down wrong.

2x-y-7=0

-3-3y=0

And solve as simultaneous equations.

(Expanding out, Re(0) and Im(0))

(Also, is the second part ok?)
Sorry, I wasn't concentrating properly. It's actually quite embarrasing that I'm doing F maths and despite that, i got those simple equations wrong. :'(
6. (Original post by JTeighty)
Sorry, I wasn't concentrating properly. It's actually quite embarrasing that I'm doing F maths and despite that, i got those simple equations wrong. :'(
That wasn't meant to be a criticism, sorry. I do it annoyingly often.
7. (Original post by Scallym)
That wasn't meant to be a criticism, sorry. I do it annoyingly often.
Don't worry, I didn't take it badly. I was just stating my stupidity.
8. Seems I'm too late. =)
9. (Original post by jumblebumble)
the real and imaginary parts of the complex number z = x + iy satisfy the equation (2-i)x - (1 + 3i)y - 7 =0

a) find the value of x and y
b) find the values of i) modulus of z ii) argz

how would i go about starting this question?

will rep - i'm just really confuddled

jb
Just out of interest, is this FP1 or FP2?
10. (Original post by JTeighty)
Just out of interest, is this FP1 or FP2?
This is FP1
11. (Original post by Longorefisher)
This is FP1
Thanks.

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