Complex Numbers by Example 

-- Section 1.4 --

 

 and 

 
Perform indicated operation.     (2 - 3i)(5 + 2i)
Write in standard form. a + bi .     

Solve

                                     Step
 (2 - 3i)(5 + 2i) = 10 + 2(2i) - 3i(5) - 3i(2i)  Use F O I L - First Outer Inner Last
= 10 + 4i - 15i - 6i2   Collect like terms
= 10 - 11i - 6(-1)   i2 = -1
= 10 - 11i + 6  
= 16 - 11i  standard form: a + bi .

Perform indicated operation.     (3 - i)2
Write in standard form. a + bi . 

[Solution]

    Perform indicated operation.     (2 + 3i) - (5 - 2i)
Write in standard form. a + bi .    

Solve

                            Step
 (2 + 3i) - (5 - 2i) =  2 + 3i - 5 + 2i  Remove Parenthesis first by distributing the minus sign across the parenthesis.
= 2 + 3i - 5 + 2i = -3 + 3i + 2i Add REAL part with REAL part 
= -3 + 3i + 2i = -3 + 5i Add IMAGINARY part with IMAGINARY part 
= -3 + 5i standard form: a + bi .

  Perform indicated operation.   (6 - 3i) - (-5 + i)
Write in standard form. a + bi .    

[Solution]

Perform indicated operation and simplify.

Solve

                              Step

Always remove radicals first 

Now Multiply
i2 = -1

The answer has a REAL part only.

  Perform indicated operation and simplify.     

[Solution]

  Perform indicated operation.   
Write in standard form. a + bi .  

Solve

Step

Multiply the numerator and the denominator by 3 - 4i (complex conjugate)

(3 + 4i)(3 - 4i) = 32 -12i + 12i - 42i2 = 9 + 16 = 25 
= 9 -16(-1) = 9 + 16  = 25 

NOTE:

 (a + bi)(a - bi) = a2 + b2 Try it!

Perform indicated operation.   
Write in standard form. a + bi .  

[Solution]

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada