Question

Explain, in complete sentences and in your own words, the answers to the following questions relating to complex numbers.

What are the characteristics of a complex number?
What is the relationship between a complex number and its conjugate?
Describe the usefulness of the conjugate and its effect on other complex numbers.

Answer 1

characteristics"
i) a+ib is the general form
a=real part
b=imazinary part

Answer 2

Part 1) The characteristics generally involve the form a + bi where a and b are real numbers. The purpose of the form is that one part is real and one part is imaginary.
Part 2) The relationship between a complex number and its conjugate is that the sign separating the two parts is the opposite. For instance, + turns to - in the conjugate.
Part 3)The purpose of the conjugate in complex numbers is to rationalize it when complex numbers are int he denominator. This forms a difference in squares pattern which makes the middle terms disappear and the i^2 number to turn into a -1 because of the cycle that i goes through.