Number Systems

Number Systems

Radical Exponents

Complex Numbers

Steps1)Write the prime factorization of your radicand2)Determine the index of the radical3)Circle the identical variables by the number that is the index. (if the index is 2 circle the variables by 2)4)The number of variable from each cirlced group will show up out side the radical symbol once.5) Anything left will remain under the radical symbol, the radical symbol will disappear.6)Multiply the numbers and variables outside the radical together.

When ,2 Is implied

1/2

64

=8

Simplifying

Write in exponential

Write in Radical

X

4/3

=

3

4

X

3

X

=

X

3/2

The numerator is always going to be the exponent of the radical. What number can be multilpied twice to get the radicand?

The denominator of the exponent is still the exponent of the radical, while the numerator is going to be the index to the radicand

This is basically the opposite of writing it in radical form. Since the index of this problem is 2 it is goint to be the denominator to the exponent of the radicand, making 3/4. Now you just need to take the X out of the radical symbol to get your answer.

5 2 3 a a

30a

2

Complex Numbers

Simplifying Radicals

=

a

30

2

The a is highlighted because it is a pare

(7-2i)+(-3+i)

+-3+1i

4-1i or 4-i

Adding and Subtracting:

Multiplying:

(4-2i) (1+7i)

4+28i-2i-14

2

-1

18+26i

Dividing:

(5-2i) (3+4i)

(3-4i)(3-4i)

=

15-20i-6i+8i9-12i-12i-16i

2

2

7 25

-26 25i

=

7-26i 25

When adding combine like terms and add

If your subtracting then you distribute, combine like terms, add.

When multiplying, first foil your problem, then combine like terms.

For dividing, start off by multplying the numerator and the denominator by the complex conjugate of the denominator. Now foil the numerator and denominator, and simplify.