Other

Question 1

How do you plot an imaginary number?

Answer 1

Use the y-axis as the axis for all values i, and the x-axis for any other values (if its not a pure imaginary number).

Question 2

What is special about graphing an imaginar number?

Answer 2

The absolute value of that number = all of the terms in that number squared (without the i), then collectively square rooted = number of units from the vertex to the point on the graph. For example:

abs. val. of 3 +4i = square root of (3^2 +4^2) = 5

Question 3

Describe complex conjugates.

Answer 3

Number PAIRS of the form a +bi are complex conjugates. A +bi and a -bi are complex conjugates (or just conjugates) of each other; to rationalize a complex denominator, you must multiply by the number’s complex conjugate.

Question 4

Define an Imaginary Number

Answer 4

Any number of the form a +bi in which a and b are real numbers, and in which b does not equal zero.

Question 5

Describe the Complex Number System

Answer 5

Natural/Counting #s: 1, 2, 3, 4
Whole Number: 0, 1, 2, 3
Integers: -2, -1, 0, 1, 2
Rational #s: Any number that can be written as a ratio (a fraction).
Irrational #s: Decimals that repeat endlessly without a pattern; includes pi and some imperfect square roots.
Real #s- rational and irrational numbers
Pure Imaginary Numbers: bi
Imaginary Numbers: a +bi
Complex Numbers: real and imaginary numbers
i: the unit whose square is -1