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Lesson 1.3.2 and 1.3.3: Adding,
Subtracting and Multiplying
Imaginary Numbers
Pages in Text
By the end of this lesson, I will be able
to answer the following questions…
1. How do find the sum or difference of complex
numbers?
2. How do I determine if a complex number is
wholly real or wholly imaginary?
3. How can imaginary numbers be used in a
simple electric series circuit?
Vocabulary
1. Series Circuit -
2. Wholly Real
3. Wholly Imaginary
4. Holy Moly
Prerequisite Skills with Practice
Simplify:
4x - 5 + 3x -13- x
(-3x + 2) + (x -10)
(-3x + 2) - (-x + 2)
Example one
Is (6 + 5i) + (8 - 3i)
wholly real or wholly
or does it have a real and
an imaginary part?
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Example two
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Is (5 + 6i ) - (5 + 3i
wholly real or wholly
or does it have a real and
an imaginary part?
9
15
)
Example three
Is (12 - i 20 ) + (-18 + 4i18 )
wholly real or wholly
or does it have a real and
an imaginary part?
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A circuit in series is a circuit
where the power flows in only
one direction and goes through
each part of the circuit. A
flashlight with two batteries is a
series circuit, because the power
goes through the batteries to the
lightbulb. The impedance
(resistance to current) of an
element can be represented
using the complex number, V + Ii,
where V is the element’s voltage
and I is the element’s current.
If two elements are used in a
circuit in series, the total
impedance is the sum of the
impedance of each element. The
following diagram of a circuit
contains two elements, 1 and 2,
in series.
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The total impedance of the
circuit is the sum of the
impedance of elements 1 and 2.
Element 1 has a voltage of 25
volts and a current of
1 milliampere. Element 2 has a voltage of
20 volts and a current of 1.5 milliamperes.
What is the total impedance of the circuit?
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Example Five:
Multiply and Simplify
i i5i
Example Six:
Multiply and Simplify
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(7 + 2i)(4 + 3i)
Example Seven:
Multiply and Simplify
(5 - i)(5 + i)
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