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FP1 Complex Numbers

My problem has been solved.
(edited 8 years ago)
Original post by chemistryboi
another method that is more efficient


Consider the arg of 1+i, and what happens when you to the arg when you raise the number to the power of 4.
(edited 8 years ago)
Original post by ghostwalker
Consider the arg of 1+i, and what happens when you to the arg when you raise the number to the power of 4.


im not sure, i^4 is equal to 1. I am without a clue on this :frown:
Original post by chemistryboi
im not sure, i^4 is equal to 1. I am without a clue on this :frown:


Ok, have you come across "arg", or the format reiθre^{i\theta} for a complex number?
Original post by ghostwalker
Ok, have you come across "arg", or the format reiθre^{i\theta} for a complex number?


I have not come across that format, my understanding of the argument is the angle (usually called theta) in radians measured anticlockwise from y=0 to the line Z
Original post by chemistryboi
I have not come across that format, my understanding of the argument is the angle (usually called theta) in radians measured anticlockwise from y=0 to the line Z


:holmes: How about the cos⁡θ+isin⁡θ\cos\theta +i\sin\theta format, and what happens when you raise it to a power?
Original post by ghostwalker
:holmes: How about the cos⁡θ+isin⁡θ\cos\theta +i\sin\theta format, and what happens when you raise it to a power?


I don't know where I have gotten this idea from but does it rotate? As in change quadrant but with a different angle
Original post by ghostwalker
Ok, have you come across "arg", or the format reiθre^{i\theta} for a complex number?


This is an FP2 formula.

Original post by chemistryboi
Hi TSR
hence show that ((2+3i)/(5+i))^4 is real and determine its value.


You know what (2+3i)/(5+i) simplifies to, just raise that to the power 4. I.E (lambda(1+i))^4 = (lambda)^4(1+i)^4
Original post by chemistryboi
I don't know where I have gotten this idea from but does it rotate? As in change quadrant but with a different angle


It does "rotate". When you multply two complex numbers together you sum their angles, so to speak.

But since you've not come across these format yet (they are covered at A-level). I suggest substitute your expression λ(1+i)\lambda (1+i), and square it, and square it again, to get the fourth power. After the first squaring, it will be a simpler format.
Original post by ghostwalker
.


Thank you for helping me out on this one. I greatly appreciate it.

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