My Learning Cart
?
Categories
Account

If z = 1 + i√3, what is |z|^2?

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If z = 1 + i√3, what is |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, what is |z|^2?

Practice Questions

Q1
If z = 1 + i√3, what is |z|^2?
  1. 4
  2. 3
  3. 2
  4. 1

Questions & Step-by-Step Solutions

If z = 1 + i√3, what is |z|^2?
  • Step 1: Identify the complex number z, which is given as z = 1 + i√3.
  • Step 2: Recall that the magnitude squared of a complex number z = a + bi is calculated using the formula |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: Therefore, |z|^2 = 4.
  • Complex Numbers – Understanding the modulus of a complex number and how to calculate it.
  • Modulus Calculation – Using the formula |z|^2 = a^2 + b^2 for a complex number z = a + bi.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks