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Tutorial 12: Complex Numbers

WTAMU > Virtual Math Lab > College Algebra > Tutorial 12: Complex Numbers


 

 

check markAnswer/Discussion to 1a

problem 1a

 
ad1a2

*Add the real num. together and the imaginary num. together
*Complex num. in stand. form 

 


 

 

check markAnswer/Discussion to 1b

problem 1b

 
ad1b

*Subtract the real num. together and the imaginary num. together
*Complex num. in stand. form 

 


 

 

check markAnswer/Discussion to 1c

problem 1c

 
Step 1:  Multiply the complex numbers in the same manner as polynomials

AND

Step 2:  Simplify the expression.

 
ad1c1

*Use dist. prop. to multiply

*i squared = -1
 

 
Step 3:  Write the final answer in standard form.

 
ad1c2

*Complex num. in stand. form

 


 

 

check markAnswer/Discussion to 1d

problem 1d

 
Step 1:  Multiply the complex numbers in the same manner as polynomials

AND

Step 2:  Simplify the expression.

 
ad1d

*Use FOIL method to multiply

*Combine imaginary numbers
*i squared = -1

 
Step 3:  Write the final answer in standard form.

 
ad1de

*Complex num. in stand. form

 


 

 

check markAnswer/Discussion to 1e

problem 1e

 
Step 1:  Find the conjugate of the denominator.

 
In general the conjugate of a + bi is a - bi and vice versa. 

So what would the conjugate of our denominator be? 

It looks like the conjugate is ad1e1.

 
 
Step 2:  Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1

AND

Step 3:  Simplify the expression.

 
ad1e6
*Multiply top and bottom by conj. of den.
 
 

*conjugate
 


 
 
 

 

 
Step 4:  Write the final answer in standard form.

 
ad1e7
 

*Divide each term of num. by 10
 
 

*Complex num. in stand. form
 

 


 

 

check markAnswer/Discussion to 1f

problem 1f

 

 
ad1f1

*Square root of a negative is i

 
Step 2:  Perform the indicated operation

AND

Step 3:  Write the final answer in standard form.

 
ad1f2

*Rewrite 50 as (25)(2) and 72 as (36)(2)

*The square root of 4 is 2 and the square root of 36 is 6
*Add like radicals: 15i + 6i = 21i
*Complex num. in stand. form (note real num. part is 0)

 


 

 

check markAnswer/Discussion to 1g

problem 1g

 

 
ad1g1

*Square root of a negative is i

 
Step 2:  Perform the indicated operation

AND

Step 3:  Write the final answer in standard form.

 
ad1g2

*i squared = -1

*Complex num. in stand. form

 


 

 

check markAnswer/Discussion to 1h

problem 1h

 

 
ad1h1

*Square root of a negative is i

 
Step 2:  Perform the indicated operation

AND

Step 3:  Write the final answer in standard form.

 
ad1h2
 
 

*Rewrite 20 as (4)(5) 
 
 

*The square root of 4 is 2
 
 

*Divide each term of num. by 2
 
 

*Complex num. in stand. form
 

 


 

 

check markAnswer/Discussion to 1i

problem 1i

 

 
ad1i1

*Square root of a negative is i

 
Step 2: Perform the indicated operation

AND

Step 3:  Write the final answer in standard form.

 
ad1i2
*i squared = -1

*Complex num. in stand. form (note that the imaginary part is 0)

 

 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 12: Complex Numbers


Last revised on Dec. 15, 2009 by Kim Seward.
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