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If z = 1 + i√3, find |z|^2.

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Question: If z = 1 + i√3, find |z|^2.

Options:

  1. 4
  2. 3
  3. 2
  4. 1

Correct Answer: 4

Solution: 

|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.

If z = 1 + i√3, find |z|^2.

Practice Questions

Q1
If z = 1 + i√3, find |z|^2.
  1. 4
  2. 3
  3. 2
  4. 1

Questions & Step-by-Step Solutions

If z = 1 + i√3, find |z|^2.
Correct Answer: 4
  • Step 1: Identify the complex number z, which is given as z = 1 + i√3.
  • Step 2: Recall the formula for the magnitude squared of a complex number z = a + bi, which is |z|^2 = a^2 + b^2.
  • Step 3: In our case, a = 1 and b = √3.
  • Step 4: Calculate a^2, which is (1)^2 = 1.
  • Step 5: Calculate b^2, which is (√3)^2 = 3.
  • Step 6: Add the results from Step 4 and Step 5: 1 + 3 = 4.
  • Step 7: Conclude that |z|^2 = 4.
  • Complex Numbers – Understanding the representation and properties of complex numbers, including their modulus.
  • Modulus of a Complex Number – Calculating the modulus of a complex number using the formula |z| = √(a^2 + b^2) where z = a + bi.
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