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Complex Number Sample Questions

Question 1: Simplify using the imaginary unit


Answer: 

Explanation: Apply the imaginary number rule.


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Question 2: Simplify using the imaginary unit


Answer: 

Explanation: Apply the imaginary number rule.


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Question 3: Simplify using the imaginary unit


Answer: 

Explanation: Apply the imaginary number rule.


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Question 4: Identify the real and imaginary part of 


Answer: Real part , imaginary part 

Explanation: Compare the equation with 


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Question 5: Multiply: 


Answer: 

Explanation: Distribute 4 inside the parenthesis.


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Question 6: Find the value of 


Answer: 1

Explanation: Plug the value of 


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Question 7: Combine: 


Answer: 

Explanation: Combine the imaginary part.


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Question 8: Multiply: 


Answer: 

Explanation: Use FOIL to distribute.


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Question 9: Plot on the complex plane.


Answer:


Explanation:  We know complex plane  is plotted as .


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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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