Write the complex number - 2+2i in polar form

For polar form you need to find the modulus (length of the vector) and the argument (angle of the vector) and present in form rcis (Arg) or re^Argi

start with the modulus r=sqrt (a^2 + b^2)

=sqrt (-2^2 + 2^2)

= sqrt (4+4)

=sqrt (8)

=2sqrt (2)

next the argument, firstly arg=tan (b/a)

= tan (2/2)

=tan (1)

=pi/4. (exact values table)

Now consider the quadrant the complex number is in, as it is (-2,2) it is in the second quadrant and as such your Arg value is:

Arg=pi-arg

= pi-pi/4

= 3pi/4

add it all together and your complex number in polar form is:

2sqrt2cis (3pi/4)

note: cis is short hand for cos (x) + isin (x), it is possible your tutor would rather you use the complex exponential form which is simply re^Argi and your answer would look like:

2sqrt2e^ (3pi/4) i

Also notice the difference between arg and Arg as this often slips students up and always present Arg in prinicple argument form ie - pi
Hopefully this has been clear enough and good luck