If z = 3 + 4i, what is the modulus of z? (2021)

₹0.0

Question: If z = 3 + 4i, what is the modulus of z? (2021)

Options:

Correct Answer: 5

Exam Year: 2021

Solution:

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

If z = 3 + 4i, what is the modulus of z? (2021)

If z = 3 + 4i, what is the modulus of z? (2021)

Step 1: Identify the complex number z, which is given as z = 3 + 4i.
Step 2: The modulus of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2).
Step 3: In our 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: Take the square root of the sum from Step 6: √25 = 5.
Step 8: Therefore, the modulus of z is 5.

Modulus of a Complex Number – The modulus of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.