Question 1: Simplify using the imaginary unit :
Answer:
Explanation: Apply the imaginary number rule.
Question 2: Simplify using the imaginary unit :
Answer:
Explanation: Apply the imaginary number rule.
Question 3: Simplify using the imaginary unit :
Answer:
Explanation: Apply the imaginary number rule.
Question 4: Identify the real and imaginary part of
Answer: Real part , imaginary part
Explanation: Compare the equation with
Question 5: Multiply:
Answer:
Explanation: Distribute 4 inside the parenthesis.
Question 6: Find the value of
Answer: 1
Explanation: Plug the value of
Question 7: Combine:
Answer:
Explanation: Combine the imaginary part.
Question 8: Multiply:
Answer:
Explanation: Use FOIL to distribute.
Question 9: Plot on the complex plane.
Answer:
Explanation: We know complex plane is plotted as
.
Question 10: Plot as a complex vector.
Answer:
Explanation: Plot as
, and connect the point with origin by a directed line segment.
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