Simple complex number question

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Homework Statement


3. Write down the (x+iy) form for the complex numbers with the following modulus and argument (in radians):
(a) Modulus 1, argument pi
(b) Modulus 3, argument -pi/3
(c)Modulus 7, argument -4



Homework Equations


Modulus = ((a)^2 + (b)^2)^1/2
Arg = the angle


The Attempt at a Solution


I'm basically just checking to see if i've got the right method.

(a)If Modulus = 1 and the argument = pi, then that would mean the angle is theta = 0. The only way to achieve this would to be if the imaginary part = 0, so the answer is:
1+0i or just 1

(b)This is where I start to get confused. If the argument = -pi/3 then I can use pythagoras to find the adjacent and hypoteneuse.
In this case:
cos(-120)*3 = a
a = -3/2

sin(-120)*3 = b
b = -3((3)^1/2)/2

This works since ((a)^2 + (b)^2)^1/2 does give me 3 in this case

(c)Modulus 7, Argument is -4, which gives me an angle of (-229.183'). So I can do the same again.

cos(-229.183)*7 = a
a = -6.918

sin(-229.183)*7 = b
b = -1.067

This once again seems to work, so my answerwould be something like -6.918 + -1.067i

I was wanting to check if this is all correct or if i've done the question completely wrong.

Thanks alot
 

Answers and Replies

  • #2
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For a) arg(1 + 0i) = 0, not pi, so 1 + 0i is not correct.

For b) your answer looks correct. An arg of -pi/3 puts the complex number in the 3rd quadrant, so both the Re part and the Im part will have negative values.

For c) your Re value is close (to get closer, use more decimal place precision in your conversion from radians to degrees) but the Im value has the wrong sign. An arg of -4 puts the complex number in the 2nd quadrant. -pi > -4 > -3pi/2, where '>' signifies "is less negative than"
 

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