(−2 + 3j)5

= (3.60555 ∠ 123.69007°)5 (converting to polar form)

= (3.60555)5 ∠ (123.69007° × 5) (applying deMoivre's Theorem)

= 609.33709 ∠ 618.45035°

= −121.99966 − 596.99897j (converting back to rectangular form)

= −122.0 − 597.0j (correct to 1 decimal place)

For comparison, the exact answer (from multiplying out the brackets in the original question) is

−122 − 597j

[Note: In the above answer I have kept the full number of decimal places in the calculator throughout to ensure best accuracy, but I'm only displaying the numbers correct to 5 decimal places until the last line.]