The complex number (2+2i)^11/(2-2i)^9 has to be simplified first.

(2+2i)^11/(2-2i)^9

=> (4 + 4i^2 + 8i)^5*(2 + 2i) / (4 +4i^2 - 8i)^4 * (2 - 2i)

=> (8i)^5*(2 + 2i) / (- 8i)^4 * (2 - 2i)

=> (64i^2)^5*(2 + 2i) / (64i^2)^4 * (2 - 2i)

=> -64*(2 + 2i) / (2 - 2i)

=> -64*(2 + 2i)(2 + 2i) / (2 - 2i)(2 + 2i)

=> -64*(2 + 2i)(2 + 2i) / (4 + 4)

=> -8*(2 + 2i)(2 + 2i)

=> -8*(4 + 4i^2 + 8i)

=> -64i

The argument of -64i is -90

The argument of the complex number is -90 degrees