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Abraham's presentation

A complex number is a number that can be put in the form of a+bi, where a and b are real numbers and i is called the imaginary number.

Topic 1

The values a and b can be zero.

Examples

1+2i, or 2-6i

Topic 2

How to write an expression as a complex number in standard form

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

Steps

Combine the like terms

Subtopic 2

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

Simplify

7+7i

Topic 3

dealing with subtraction

Text

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

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

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

=5-i

the negative has to be put into the 2nd group and then you will be able to simplify the problem.

Picture

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

Topic 4

Simplify

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

(4+3)+(-1+2)i=

7+i

Title

complex numbers are multiplied in the same way as polynomials. All terms of one complex number must be multiplied by all terms of the other.

Title

i2= -1 and use this to simplify the result.

Multiply 5i(2 + 3i).

Title

Solution:

5i(2 + 3i) = 10i + 15i^2

= 10i + 15(-1)

=-15 + 10i

-Use the distributive property

-Replace i^2 with -1

-put in standard form

Title

Multiply (9 –i)(2 + 5i).

Title

(9 –i)(2 + 5i)

= 18 + 45i –2i –5i^2

= 18 + 43i –5(-1)

=23 + 43i

-FOIL

-Collecting like terms and replacing i^2 with -1

-Collect like terms

Title

Powers of i

The imaginary number, i, when raised to a power can be simplified to one of 4 results: 1, i, -1, or –i.

Title

i = i

i^2= -1

i^3= i^2∙i= -i

i^4= i^2∙i^2= -1 ∙ -1 = 1

i^5=i^4∙i= i

Title

Since i^4m= 1,where m is any whole number, then to simplify powers of i, rewrite the problem as ito the 4thpower (or a multiple of 4) times the remaining power needed.

Title

i^22

Rewrite as i^22 = i^20∙ i^2= i^2= -1

i^100

Title

Since 100 is a multiple of 4, i^100= 1.

Simplify

Title

(3-2i)-(4-6i)

(3-2i)- 4+6i

-1+4i

distribute through, only multiply when using multiplication

5i(8-3i)

=40i-15i^2

=40i-15(-1)

=40i+15

=15+40i

you have to write the real part first the the # with the imaginary part

Title

Simplify

(4+i)+(3-9i)

=7-8i

Title

(8+3i)(2+9i)

=16i+72i+6i+27i

=-11+72i+6i

=-11=78i

Title

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