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If z = 2e^(iπ/4), then z^2 is?

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Question: If z = 2e^(iπ/4), then z^2 is?

Options:

  1. 4e^(iπ/2)
  2. 4e^(iπ/4)
  3. 2e^(iπ/2)
  4. 2e^(iπ/4)

Correct Answer: 4e^(iπ/2)

Solution: 

z^2 = (2e^(iπ/4))^2 = 4e^(iπ/2).

If z = 2e^(iπ/4), then z^2 is?

Practice Questions

Q1
If z = 2e^(iπ/4), then z^2 is?
  1. 4e^(iπ/2)
  2. 4e^(iπ/4)
  3. 2e^(iπ/2)
  4. 2e^(iπ/4)

Questions & Step-by-Step Solutions

If z = 2e^(iπ/4), then z^2 is?
  • Step 1: Start with the given value of z, which is z = 2e^(iπ/4).
  • Step 2: To find z^2, we need to square the entire expression: z^2 = (2e^(iπ/4))^2.
  • Step 3: When squaring a product, we can square each part separately: (2^2) * (e^(iπ/4))^2.
  • Step 4: Calculate 2^2, which equals 4.
  • Step 5: Now, calculate (e^(iπ/4))^2. When you square an exponent, you multiply the exponent by 2: e^(iπ/4 * 2) = e^(iπ/2).
  • Step 6: Combine the results from Step 4 and Step 5: z^2 = 4 * e^(iπ/2).
  • Complex Numbers – Understanding the representation of complex numbers in exponential form and how to manipulate them.
  • Exponential Functions – Applying properties of exponents, particularly in the context of complex numbers.
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