In polar representation, a complex number is represented in terms of two variables r and t, where r is the modulus of complex number and t is the angle with the positive direction of x-axis.
We know that the modulus of a complex number z=a+ib is denoted by |z| and is defined as 
. We also know that the point P(a,b) is the representation of the complex number a+bi in a coordinate plane.
Then from the above figure,
Cos t = a/r ==> a = r Cost
Sin t = b/r ==>b= r Sint,
where t is the angle in radians which is called the argument of a+bi.
and we have tant = b/a==> t = tan-1(b/a)
Aslo, from trigonometric Pythagorean identity, we have
Cos2t +Sin2t = 1
a2/r2 + b2/r2 = 1
r2 = a2+b2
r = √(a2+b2). So, r is nothing but the modulus of a+bi.
Thus, we can write a complex number a+bi as follows.
a+bi= r(Cost + i Sin t), where
r= √ a2+b2
and t = tan-1(b/a).
The above representation is called polar form of a+ib.
Converting a given complex number into polar form:
(1) Find r = √ a2+b2
(2) Find t = tan-1(b/a).
(3) Substitute r and t in the polar form r(Cos t + i Sint)
Example:
1) i = 1 (Cos π/2 + i Sin π/2).
2) 1+I
R = √ a2+b2=√2
t = tan-1(b/a)= tan-1(1)=π/4.
So, 1+I = √2 (Cos π/4 + i Sin π/4)
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Example image courtesy of https://www.ping.be/~ping1339/complget.htm