Final answer:
To find the modulus and argument after raising (√3)[cos ( π /18 )+isin ( π /18 )] to the 6th power, multiply the modulus by itself and multiply the argument by 6. The modulus is √18 and the argument is π /3.
Step-by-step explanation:
To find the modulus and argument after raising (√3)[cos ( π /18 )+isin ( π /18 )] to the 6th power, we need to multiply the modulus by itself and multiply the argument by 6. The modulus of (√3)[cos ( π /18 )+isin ( π /18 )] is √3 because √3 multiplied by its conjugate (√3)[cos (-π /18 )-isin ( π /18 )] gives us 3. To find the argument after raising to the 6th power, we multiply the original argument (π /18) by 6, which gives us π /3. Therefore, the correct answer is: b. modulus = √18; argument = π /3.