Question

What are the characteristics of a complex number? (1 point)
What is the relationship between a complex number and its conjugate? (2 point)
Describe the usefulness of the conjugate and its effect on other complex numbers. (2 points)

Answer 1

A complex number is a number of the form
a + bi,
where a and b are real numbers, and i is defined as i^2 = -1

Answer 2

For complex number a + bi, its complex conjugate is a - bi.

Answer 3

A complex number may have b = 0, in which case it's purely real.
For a complex number in which b is not zero, i.e., it does have an imaginary part, then by multiplying it by its complex conjugate the product is a real number.

Answer 4

Thanks! but what about equations like this one...

Answer 5

A complex number is made up of both real and imaginary components. It can be represented by an expression of the form (a+bi), where a and b are real numbers and i is imaginary. When defining i we say that\[i=\sqrt{-1}\]

Answer 6

A fraction with a complex number in the denominator is not considered to by siplified. Taking advantage of the fact that by multiplying a complex number by its complex conjugate you get a purely real number, to simplify a fraction that has a complex number in the denominator, multiply the numerator and denominator of the fraction by the complex conjugate of the denominator. The denominator becomes real and the fraction is considered to be simplified.

Answer 7

\[\frac{ √-49 }{ (3+4i)-(2-5i)}\]

Answer 8

that was the hardest question

Answer 9

First, simplify the denominator.
Also, simplify the numerator/

Answer 10

i got 63 + 7i/ 82

Answer 11

correct

Answer 12

Thank you :D

Answer 13

Gave ya a medal