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If z = 3 + 4i, what is the value of |z|^2? (2019)

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Question: If z = 3 + 4i, what is the value of |z|^2? (2019)

Options:

  1. 25
  2. 7
  3. 12
  4. 16

Correct Answer: 25

Exam Year: 2019

Solution: 

|z|^2 = 3^2 + 4^2 = 9 + 16 = 25.

If z = 3 + 4i, what is the value of |z|^2? (2019)

Practice Questions

Q1
If z = 3 + 4i, what is the value of |z|^2? (2019)
  1. 25
  2. 7
  3. 12
  4. 16

Questions & Step-by-Step Solutions

If z = 3 + 4i, what is the value of |z|^2? (2019)
  • Step 1: Identify the complex number z, which is given as z = 3 + 4i.
  • Step 2: Recall that the magnitude (or modulus) of a complex number z = a + bi is calculated using the formula |z| = sqrt(a^2 + b^2).
  • Step 3: In this case, a = 3 and b = 4.
  • Step 4: Calculate a^2, which is 3^2 = 9.
  • Step 5: Calculate b^2, which is 4^2 = 16.
  • Step 6: Add the results from Step 4 and Step 5: 9 + 16 = 25.
  • Step 7: The value of |z|^2 is equal to 25.
  • Complex Numbers – Understanding the representation of complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
  • Magnitude of Complex Numbers – Calculating the magnitude (or modulus) of a complex number, which is given by the formula |z| = √(a^2 + b^2).
  • Square of the Magnitude – Knowing that |z|^2 = a^2 + b^2 directly without taking the square root.
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