I have some complex numbers I need to find modulus and argument for.

- (1+√3i)(1-√3i)
- z = a+bi = 1-√3i+√3i+3 = 4
- lzl = √(a^2 + b^2) = √4^2 = √16 = 4
- arg(z) = tan-1(b/a) = tan-1(0/4) = 0 degrees

- conjugate -i
- conjugate -i = i
- lzl = √(a^2 + b^2) = √1^2 = √1 = 1
- arg(z) = tan-1(b/a) = tan-1(1/0) = 90 degrees

- 1-i/1-i
- z = a+bi = 1-i/1-i = (1-i)*(1+i)/(1-i)*(1+i) = 1+i-i-i^2/1+i-i-i^2 = 1+i-i+1/1+i-i+1 = 2/2 = 1
- lzl = √(a^2 + b^2) = √1^2 = √1 = 1
- arg(z) = tan-1(b/a) = tan-1(1/0) = 90 degrees

Is the calculations I did correct? - I think that the last one is wrong, but I just cant figure out why ..

Guest Jan 28, 2015