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further maths complex numbers quick question! +rep

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
Reply 1
Avatar for JTeighty
JTeighty
2
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...
Reply 2
Avatar for jumblebumble
jumblebumble
OP
10
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
Reply 3
Avatar for Scallym
Scallym
JTeighty's method is right, it's just that he's written the equations down wrong.

Start with:

2x-y-7=0

-3-3y=0

And solve as simultaneous equations. :smile:

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

(Also, is the second part ok?)
Reply 4
Avatar for JTeighty
JTeighty
2
Scallym
JTeighty's method is right, it's just that he's written the equations down wrong.

Start with:

2x-y-7=0

-3-3y=0

And solve as simultaneous equations. :smile:

(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. :'(
Reply 5
Avatar for Scallym
Scallym
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.:p:
Reply 6
Avatar for JTeighty
JTeighty
2
Scallym
That wasn't meant to be a criticism, sorry. I do it annoyingly often.:p:


Don't worry, I didn't take it badly. I was just stating my stupidity.
Seems I'm too late. =)
Reply 8
Avatar for JTeighty
JTeighty
2
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?
JTeighty
Just out of interest, is this FP1 or FP2?


This is FP1
Reply 10
Avatar for JTeighty
JTeighty
2
Longorefisher
This is FP1


Thanks.

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