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Multiplying and Dividing Complex Numbers
The Lesson Activities will help you meet these educational goals:
- Mathematical Practices—You will make sense of problems and solve them.
- Inquiry—You will perform an investigationin which you will analyze results and communicate your results in written form.
- 21stCentury Skills—You will use critical-thinking and problem-solving skills and communicate effectively.
Directions
Save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.
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Self-Checked Activities
Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.
- Multiplying and Dividing Complex Numbers
Simplify the given terms, and write the answers in standard form.
- (3 − 2i)2 − 3(i − 2) + 5
Sample answer:
(3 − 2i)2 − 3(i − 2) + 5
= (9 − 12i + 4i2) − 3i + 6 + 5[(a + b)2 = a2 + 2ab + b2]
= 9 − 12i + 4 (-1) − 3i + 11[i2 = -1]
= 9 − 12i− 4 − 3i + 11
= 16 − 15i
- (2 −)(-3 + )
Sample answer:
(2 −)(-3 + )
= (2 −)(-3 + )
= (2 −)(-3 + )[]
= (2 − 7i)(-3 + 2i)
= (2)(-3) + (2)(2i) + (-7i)(-3) + (-7i)(2i)[using FOIL]
= -6 + 4i + 21i − 14i2
= -6 + 4i + 21i − 14(-1)[i2 = -1]
= -6 + 25i + 14
= 8 + 25i
Sample answer:
=
= []
=
=
=
=
= [i2 = −1]
=
=
= i
= 0 + 1i
- (4 + 3i)2 − (7 + i)(5 − 4i)
Sample answer:
(4 + 3i)2 − (7 + i)(5 − 4i)
= (16 + 24i + 9i2) – [(7)(5) + (7)(−4i) + (i)(5) + (i)(-4i)][(a + b)2 = a2 + 2ab + b2, FOIL]
= [16 + 24i + 9i2] − [35 − 28i + 5i − 4i2]
= [16 + 24i + 9(-1)] − [35 − 23i − 4(-1)][i2 = −1]
= 16 + 24i − 9 − 35 + 23i − 4
= −32 + 47i
Sample answer:
= [(a + b)2 = a2 + 2ab + b2, FOIL]
=
= [i2 = −1]
=
=
= [i2 = −1]
=
=
=
=
= [i2 = −1]
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