# FP2: complex numbers

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both complex numbers give me the same answer, for part c....

Last edited by Maths&physics; 1 year ago

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#2

I don't follow which part of the question you're trying to answer / what you're having trouble with?

Some bits of the answer (1st equation) don't make sense - the complex number does not equal its angle?

Some bits of the answer (1st equation) don't make sense - the complex number does not equal its angle?

(Original post by

both complex numbers give me the same answer.

**Maths&physics**)both complex numbers give me the same answer.

Last edited by mqb2766; 1 year ago

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(Original post by

I don't follow which part of the question you're trying to answer / what you're having trouble with?

Some bits of the answer (1st equation) don't make sense - the complex number does not equal its angle?

**mqb2766**)I don't follow which part of the question you're trying to answer / what you're having trouble with?

Some bits of the answer (1st equation) don't make sense - the complex number does not equal its angle?

sorry, I rushed it a little to make it eligible for TSR....

it was arg ((x -6) +iy) = [-3(pi)]/4

Last edited by Maths&physics; 1 year ago

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(Original post by

What did you get for a) and b)?

**mqb2766**)What did you get for a) and b)?

b was drawing the half line....

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#6

So c) is asking for the complex number which satisfies both a) and b). Should be easy to sketch, I'm presuming you just need to do the numbers to get the value?

Your working in the attached image seems very confused (argument incorrect, center 4,4, ...). What are you trying to do?

Your working in the attached image seems very confused (argument incorrect, center 4,4, ...). What are you trying to do?

(Original post by

I got them both right: centre: (4, -2) and radius (root)20

b was drawing the half line....

**Maths&physics**)I got them both right: centre: (4, -2) and radius (root)20

b was drawing the half line....

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#7

I'm not sure what you mean?

I got the same values of x and y for part c

X = 4 +/- sqrt 10

Y = -2 +/- sqrt 10

I got the same values of x and y for part c

X = 4 +/- sqrt 10

Y = -2 +/- sqrt 10

(Original post by

both complex numbers give me the same answer, for part c....

**Maths&physics**)both complex numbers give me the same answer, for part c....

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(Original post by

So c) is asking for the complex number which satisfies both a) and b). Should be easy to sketch, I'm presuming you just need to do the numbers to get the value?

Your working in the attached image seems very confused (argument incorrect, center 4,4, ...). What are you trying to do?

**mqb2766**)So c) is asking for the complex number which satisfies both a) and b). Should be easy to sketch, I'm presuming you just need to do the numbers to get the value?

Your working in the attached image seems very confused (argument incorrect, center 4,4, ...). What are you trying to do?

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(Original post by

I'm not sure what you mean?

I got the same values of x and y for part c

X = 4 +/- sqrt 10

Y = -2 +/- sqrt 10

**ohemgee11**)I'm not sure what you mean?

I got the same values of x and y for part c

X = 4 +/- sqrt 10

Y = -2 +/- sqrt 10

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#11

Oh okay!

I

But if they're looking for only one I can't remember how to find the 'correct' answer if there is a way to do so

Maybe others who are more advanced can help

Sorry about that haha

I

*am*a bit rusty at Further maths at the moment but maybe they want you to combine the two results into one complex number?But if they're looking for only one I can't remember how to find the 'correct' answer if there is a way to do so

Maybe others who are more advanced can help

Sorry about that haha

(Original post by

when I subbed y = x - 6 into the equation of the circle, that's what you get and solving for x gave me the right x value but it gave me 2 and I didn't know which one was the right one. yeah, I am very confused by this question

**Maths&physics**)when I subbed y = x - 6 into the equation of the circle, that's what you get and solving for x gave me the right x value but it gave me 2 and I didn't know which one was the right one. yeah, I am very confused by this question

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#12

(Original post by

so, I got cartesian form y = x - 6 from the second equation and subbed that into the circle equation and I got the right value for x..... but I got 2 values and I don't know which one is the right one and why...

**Maths&physics**)so, I got cartesian form y = x - 6 from the second equation and subbed that into the circle equation and I got the right value for x..... but I got 2 values and I don't know which one is the right one and why...

I think I found it

Of your two complex numbers, one is in the 1st quadrant, and the other is in the 3rd quadrant (just sketch them quickly on an argand diagram). The one in the first quadrant gives you an argument of pi/4

The one in the 3rd quadrant gives you -3pi/4. This is the one you're looking for

So z= 4 - sqrt 10 + (-2-sqrt 10)i

This is the complex number such that arg (z-6) = -3pi/4

Last edited by ohemgee11; 1 year ago

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(Original post by

Oh oops!

I think I found it

Of your two complex numbers, one is in the 1st quadrant, and the other is in the 3rd quadrant (just sketch them quickly on an argand diagram). The one in the first quadrant gives you an argument of pi/4

The one in the 3rd quadrant gives you -3pi/4. This is the one you're looking for

So z= 4 - sqrt 10 + (-2-sqrt 10)i

This is the complex number such that arg (z-6) = -3pi/4

**ohemgee11**)Oh oops!

I think I found it

Of your two complex numbers, one is in the 1st quadrant, and the other is in the 3rd quadrant (just sketch them quickly on an argand diagram). The one in the first quadrant gives you an argument of pi/4

The one in the 3rd quadrant gives you -3pi/4. This is the one you're looking for

So z= 4 - sqrt 10 + (-2-sqrt 10)i

This is the complex number such that arg (z-6) = -3pi/4

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#14

Did you subtract 6 from Re(z)?

(Original post by

when you solve this for theta, it doesn't give -3pi/4?

**Maths&physics**)when you solve this for theta, it doesn't give -3pi/4?

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what do you mean?

those values you said are the right answer (which they are) dont = -3pi/4 after you've drawn the diagram with those values.

those values you said are the right answer (which they are) dont = -3pi/4 after you've drawn the diagram with those values.

(Original post by

Did you subtract 6 from Re(z)?

**ohemgee11**)Did you subtract 6 from Re(z)?

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#16

Yea the -3pi/4 comes from arg(z - 6) not arg(z)

So in this case arg(z-6) =arg ((-2- sqrt 10) + (-2-sqrt 10)i)

This will give you -3pi/4

So in this case arg(z-6) =arg ((-2- sqrt 10) + (-2-sqrt 10)i)

This will give you -3pi/4

(Original post by

what do you mean?

those values you said are the right answer (which they are) dont = -3pi/4 after you've drawn the diagram with those values.

**Maths&physics**)what do you mean?

those values you said are the right answer (which they are) dont = -3pi/4 after you've drawn the diagram with those values.

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(Original post by

Yea the -3pi/4 comes from arg(z - 6) not arg(z)

So in this case arg(z-6) =arg ((-2- sqrt 10) + (-2-sqrt 10)i)

This will give you -3pi/4

**ohemgee11**)Yea the -3pi/4 comes from arg(z - 6) not arg(z)

So in this case arg(z-6) =arg ((-2- sqrt 10) + (-2-sqrt 10)i)

This will give you -3pi/4

and not: ((-2 + sqrt 10) + (-2 + sqrt 10)i)

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#19

The argument of the second one is pi/4

The reason why you get two answers is because when you find the equation of the half line, you apply the tangent of -3pi/4, right?

Tan (-3pi/4) gives 1, but as you know, there is more than 1 angle that will also give tan (theta) is 1

So when we find x, we get two answers. These two answers will work for the circle equation, but only one will work for the half line, because only one has an argument of -3pi/4. The other has an argument of pi/4.

The one with an argument of -3pi/4 is the one you should use

The reason why you get two answers is because when you find the equation of the half line, you apply the tangent of -3pi/4, right?

Tan (-3pi/4) gives 1, but as you know, there is more than 1 angle that will also give tan (theta) is 1

So when we find x, we get two answers. These two answers will work for the circle equation, but only one will work for the half line, because only one has an argument of -3pi/4. The other has an argument of pi/4.

The one with an argument of -3pi/4 is the one you should use

(Original post by

why: ((-2- sqrt 10) + (-2-sqrt 10)i)

and not: ((-2 + sqrt 10) + (-2 + sqrt 10)i)

**Maths&physics**)why: ((-2- sqrt 10) + (-2-sqrt 10)i)

and not: ((-2 + sqrt 10) + (-2 + sqrt 10)i)

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