Mr. Sims
Algebra 2
Section 8.2 A
Products and Quotients
of Complex Numbers
Imaginary Number Rules
2
i  1 and
1  i
Simplify each product.
1. 6i · 7i
= 42i2
= 42(-1)
= - 42
3.  3  2  4  11
 3  1 2  4  1 11
 3i 2  4i 11
2. i 3  i 2  i 6
 i3 36
 i2  i  6
= (-1)(i)(6)
= -6i
must factor –1 out
before multiplying
 12i 2 22
 12(1) 22
 12 22
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2
4. 2  6  4  2
 2 1 6  4 1 2
 2i 6  4i 2
 8i 2 12
 8(1) 4 3
 8(2) 3
 16 3
i  1 and
1  i
factor –1 out
before multiplying
5.
 5   10   2
  1 5   1 10   1 2
break down
before multiplying
 i 5  i 10  i 2
 i3 100
 i 2  i(10)
 (1)(i)(10)
 10i
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6.
2
i  1 and
3 6( 2   10)
 3 6( 2   1 10)
1  i
break down
before multiplying
 3 6( 2  i 10)
 3 12  3i 60
distributive property
 3 4 3  3i 4 15
 3(2) 3  3i(2) 15
 6 3  6i 15
7. (4 + 3i)(5 + 6i)
= 4(5) + 4(6i) + 3i(5) + 3i(6i) foil method
= 20 + 24i + 15i + 18i2
= 20 + 39i + 18(-1) combine like terms
= 20 + 39i – 18
= 2 + 39i
Mr. Sims
2
i  1 and
1  i
8. (6 – 5i)(-3 + i)
= 6(-3) + 6i – 5i(-3) – 5i(i) foil method
= -18 + 6i + 15i – 5i2
= -18 + 21i –5(-1) combine like terms
= -18 + 21i + 5
= -13 + 21i
9. (4 + 5i)2
= (4 + 5i)(4 + 5i)
= 4(4) + 4(5i) + 5i(4) + 5i(5i) foil method
= 16 + 20i + 20i + 25i2
= 16 + 40i + 25(-1) combine like terms
= 16 + 40i – 25
= -9 + 40i
Mr. Sims
10. (-5 – i)2
= (-5 – i)(-5 – i)
= -5(-5) – 5(-i) – i(-5) – i(-i) foil method
= 25 + 5i + 5i + i2
= 25 + 10i – 1 combine like terms
= 24 + 10i
11. i 3 
4
 i 4 34
 i2  i2  81
= (-1)(-1)(9)
=9
Mr. Sims
Algebra 2
Section 8.2 A
Assignment
Simplify each product.
1.)  i 3  i 5
2.)
5   6
3.) 2 3  3  2
4.)  4 15  2 6
5.)
3  2 6  i 15 
6.)
7.) (3 – 4i)(2 + 2i)
8.) (9 + 11i)(9 – 11i)
9.) (-3 + 4i)(-3 – 4i)
10.) (6 – 2i)2
11.) (- 4i)3
12.) (-2i)5


 6  11   3 


Mr. Sims
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