What is the complex function of f(z)=\frac{1}{z}?

kihanja20

kihanja20

Answered question

2022-01-18

What is the complex function of f(z)=1z?

Answer & Explanation

Jenny Bolton

Jenny Bolton

Beginner2022-01-19Added 32 answers

It is a function that takes a complex value z0 and returns the value 1z.
Because it is a complex function, it has alternate representations.
First, as we can write any complex number z as z=a+ib, where a and b are real numbers, we have that
f(z)=1z=1a+ibaibaib=aiba2+b2=aa2+b2iba2+b2
The other representations occurs when we take z=eiθ=cosθ+isinθ. In this case, we have that f(z)=eiθ.

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