If z = re^(iθ), what is the value of r if z = 1 + i?
Practice Questions
1 question
Q1
If z = re^(iθ), what is the value of r if z = 1 + i?
√2
1
2
0
r = |z| = √(1^2 + 1^2) = √2.
Questions & Step-by-step Solutions
1 item
Q
Q: If z = re^(iθ), what is the value of r if z = 1 + i?
Solution: r = |z| = √(1^2 + 1^2) = √2.
Steps: 7
Step 1: Identify the complex number z. Here, z = 1 + i.
Step 2: Recall that in the form z = re^(iθ), r represents the magnitude (or absolute value) of z.
Step 3: To find r, we need to calculate the magnitude of z, which is given by the formula |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.
Step 4: In our case, the real part a = 1 and the imaginary part b = 1.
Step 5: Substitute the values into the formula: |z| = √(1^2 + 1^2).
Step 6: Calculate 1^2, which is 1, and then add it to the other 1^2, which is also 1. So, we have 1 + 1 = 2.
