Hi. I need to find modulus and arguement of the following complex number:
z = -sqrt(2) - sqrt(2i)
I use the following rule to find modulus: \z\ = sqrt(x^2+y^2)
I use the following rule to find argument: arg(z) = tan^-1(y/x)
Please help.
a + bi = -√2 - √2i (the "i" isn't under the root)
The modulus is given by l z l = √ (a^2 + b^2) = √[(-√2)^2 + (-√2)^2 ] = √(2 + 2) = √4 = 2
And the arg(z), Θ, is given by
tan-1 (b/a) = tan -1 (-√2/-√2) = tan-1(1) = 5pi/4 + n(2pi) .... for n = 0,±1,±2, ±3, ±4...
{remember that we're in the 3rd quadrant}
a + bi = -√2 - √2i (the "i" isn't under the root)
The modulus is given by l z l = √ (a^2 + b^2) = √[(-√2)^2 + (-√2)^2 ] = √(2 + 2) = √4 = 2
And the arg(z), Θ, is given by
tan-1 (b/a) = tan -1 (-√2/-√2) = tan-1(1) = 5pi/4 + n(2pi) .... for n = 0,±1,±2, ±3, ±4...
{remember that we're in the 3rd quadrant}
Thank you so much! - you are a lifesaver!
I have also some other complex numbers I need to find modulus and argument for.
Is the calculations I did correct? - I think that the last one is wrong, but I just cant figure out why ..