How Do You Calculate Modulus and Perform Operations on Complex Numbers?

[alpha01]

we have z = 5+2i

how do i find the following:

|z|
z^-1


i can do the basic operations (x, /, +, -) with complex numbers but i have no idea where to even start with these 2.

 

[Pere Callahan]

For a complex number z=a+ib, the conjugate is defined as $\bar z=a-ib$. |z| is the absolute value of z, the distance of z to the origin in the complex plane, and can be calculated as $|z|^2=z\bar z=a^2+b^2$. $z^{-1}$ is the inverse of z, defined by the property that $zz^{-1}=1$, so $z^{-1}=\frac{a-ib}{a^2+b^2}$

 

[fayeshin]

set z=a+bi, then |z|=sqrt(a*a+b*b)...then you can do the first one.
for the second one, it is 1/z.
1/z=1/(5+2i)=(5-2i)/29