Simple complex number question

[Crosshash]

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

 

[Mark44]

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 I am 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 I am 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"