This question can be broken into 3 steps:

1. Write the multiplicative inverse of the given complex number { in this case it is 1/(5-11i) }

2. "Use complex conjugates to simplify": this means multiplying the numerator and denominator of 1/(5-11i) by the complex conjugate of the denominator, which is found by changing the sign of the imaginary component. { this complex conjugate is 5+11i, so the simplification for this is set up like so: (1/(5-11i)) *((5+11i)/(5+11i)) }

3. Check the answer to part 2 by multiplying it by 5-11i, and it is correct if you get 1 as your answer. { you should have (5+11i)/146 as your answer to part 2, and you will indeed find that this answer multiplied by (5-11i) is equal to 1 }

You will need a good grasp on some foundational concepts such as the distributive property and order of operations; let me know if you need help with these :)

Michael K.

02/10/21