My Learning Cart
?
Categories
Account

If z = 3 + 4i, then |z| is equal to?

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

What’s inside this PDF?

Question: If z = 3 + 4i, then |z| is equal to?

Options:

  1. 5
  2. 7
  3. 25
  4. 12

Correct Answer: 5

Solution: 

The modulus |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

If z = 3 + 4i, then |z| is equal to?

Practice Questions

Q1
If z = 3 + 4i, then |z| is equal to?
  1. 5
  2. 7
  3. 25
  4. 12

Questions & Step-by-Step Solutions

If z = 3 + 4i, then |z| is equal to?
  • Step 1: Identify the complex number z, which is given as z = 3 + 4i.
  • Step 2: Recognize that the modulus |z| is calculated using the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.
  • Step 3: In our case, a = 3 and b = 4.
  • Step 4: Substitute the values into the formula: |z| = √(3^2 + 4^2).
  • Step 5: Calculate 3^2, which is 9.
  • Step 6: Calculate 4^2, which is 16.
  • Step 7: Add the results from Step 5 and Step 6: 9 + 16 = 25.
  • Step 8: Take the square root of 25: √25 = 5.
  • Step 9: Conclude that |z| is equal to 5.
  • 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.
  • Modulus of a Complex Number – Calculating the modulus (or absolute value) of a complex number using the formula |z| = √(a^2 + b^2).
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