## Practice problem3

In this page practice problem3, we will see how to multiply two complex numbers.

Solution:

1. (2+3i)(4-7i)

We are going to use FOIL method here. We can use distributive method also for multiplication of two complex numbers.

=  [(2x4)+(2x(-7i))+(3ix4)+(3ix(-7i))]

= [8+(-14i)+12i+(-21i2]

= 8-14i+12i-21(-1)

= 8-2i+21

=  29-2i

The above method is FOIL method. We can do the same problem using distributive method also.

(2+3i)(4-7i)

The distribution method is as follows:

=  2(4-7i)+3i(4-7i)

=   2x4 + 2x(-7i) +3i(4) + 3i(-7i)

=   8 -14i +12i -21(-1)

=   8+21-2i

=    29-2i

2.  (4-2i)(3-5i)

We are going to use FOIL method to do the multiplication.

=  [(4x3)+(4x(-5i))+((-2i)x3)+((-2i)(-5i))]

= [12 +(-20i)+(-6i)+10i2]

= 12-20i-6i+10(-1)

=  12 -26i -10

=   2-26i

3.   (-5+3i)(-2+i)

We are going to use FOIL method to do the multiplication.

= [((-5)(-2))+((-5)xi)(3i(-2))+(3ixi)]

= [10+(-5i)+(-3i) + 6i2]

=  10 -5i -6i+3(-1)

=   10 -11i -3

=    7-11i

4. (3-i)(8+7i)

We are going to use FOIL method to do the multiplication.

= [(3x8)+(3x(7i))+((-i)x8)+((-i)x(7i))]

= [24 +21i+(-8i)+(-7i2)]

= 24+21i-8i-7(-1)

= 24+13i+7

=  31+13i

Parents and teachers can guide the students to work out the problems discussed in practice problem3, and ask them to solve the problems given below. Teachers can guide the students to use both FOIL method and distributive method for the worked out problems as well as problems given below for practice.

Problems for practice:

1.         Multiply (3+5i) and (8-9i)
2.         Multiply (7-9i) and (12+2i)

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