1. The conjugate of a complex constant is what we get when we change i to -i.
The conjugate of -14 + 11 i is simply
Answer: -14 - 11 i choice A
2. The product of complex conjugates is the squared magnitude, which is the sum of squares of the real part and the imaginary part. It will always be real.
Let's work it out a few ways. FOIL first:
[tex]( \sqrt 3+i)( \sqrt 3-i) = \sqrt{3} \sqrt{3} -i \sqrt{3} + i \sqrt{3} - i^2 = 3 + 1 = 4[/tex]
Now just as the sum of squares of the real part and the imaginary part:
[tex]( \sqrt 3+i)( \sqrt 3-i) = |\sqrt{3} + i|^2 = (\sqrt{3})^2 + 1^2 = 3+1=4[/tex]
Choice D
