The main advantage of Euler's form - other than its beauty - is that it makes multiplying complex numbers much easier:

In words, when we multiply two complex numbers the arguments add and the moduli multiply.

Similarly for division:

In words, when we divide one complex number from another, we subtract the arguments and divide the moduli.

Example

Given that z⋅(1+i)=(2−2i), find z.

First convert everything to Euler's form: