6. Convert 3−i into polar form and hence evaluate {(3 - i)}^(7) ​

Question

6. Convert 3−i into polar form and hence evaluate


`{(3 - i)}^(7)`


​

Answer 1

9514 1404 393

Answer:

≈ 1000√10∠-129.04464° = -1992 -2456i

Explanation:

3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°

Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°

= 1000√10(cos(-129.04464°) +i·sin(-129.04464°))

= -1992 -2456i