Question: What is the value of |z| if z = -3 + 4i?
Options:
5
7
4
3
Correct Answer: 5
Solution:
|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.
What is the value of |z| if z = -3 + 4i?
Practice Questions
Q1
What is the value of |z| if z = -3 + 4i?
5
7
4
3
Questions & Step-by-Step Solutions
What is the value of |z| if z = -3 + 4i?
Step 1: Identify the complex number z, which is given as z = -3 + 4i.
Step 2: Recall that the value of |z| (the magnitude of z) is calculated using the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part of z.
Step 3: In our case, the real part a is -3 and the imaginary part b is 4.
Step 4: Substitute the values of a and b 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: Therefore, the value of |z| is 5.
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