As you may have guessed, we can write any complex number in terms of its modulus and argument, instead of its Cartesian coordinates (remember that its Cartesian coordinates are simply the real and imaginary parts of the complex number).
So for example, think about the complex number 3+3i.
We know that its modulus is the square root of 32+32, which is about 4.2 and that its argument is 45o, which is p/4 in radians.
Here's the crunch. We can write 3+3i as:
4.2cos(p/4) + 4.2 i sin(p/4).
More generally, we can write any complex number in two different ways, either
x+iy
OR
rcos(q)+irsin(q),
We can also write this second form as
r(cos(q)+isin(q)).
The form of writing a complex number that involves r and q rather than x and y is called the polar form of the complex number.