Complex

analysis

traditionally

known

as

the

theory

of

functions

of

a

complex

variable

is

the

branch

of

mathematical

analysis

that

investigates

functions

of

complex

numbers

It

is

useful

in

many

branches

of

mathematics

including

algebraic

geometry

number

theory

analytic

combinatorics

applied

mathematics

as

well

as

in

physics

including

hydrodynamics

and

thermodynamics

and

also

in

engineering

fields

such

as

nuclear

aerospace

mechanical

and

electrical

engineering