Question: If z = re^(iθ), then the value of |z| is?
Options:
r
θ
re
1
Correct Answer: r
Solution:
The modulus |z| = r in the polar form z = re^(iθ).
If z = re^(iθ), then the value of |z| is?
Practice Questions
Q1
If z = re^(iθ), then the value of |z| is?
r
θ
re
1
Questions & Step-by-Step Solutions
If z = re^(iθ), then the value of |z| is?
Step 1: Understand that z is given in polar form as z = re^(iθ).
Step 2: Recognize that in this form, 'r' represents the modulus (or absolute value) of the complex number z.
Step 3: Recall that the modulus |z| is defined as the distance from the origin in the complex plane.
Step 4: Since 'r' is the coefficient in front of e^(iθ), it directly represents the modulus |z|.
Step 5: Conclude that the value of |z| is simply r.
Polar Form of Complex Numbers – Understanding that a complex number can be expressed in polar form as z = re^(iθ), where r is the modulus and θ is the argument.
Modulus of a Complex Number – The modulus |z| of a complex number is the distance from the origin in the complex plane, which corresponds to the value r in the polar representation.
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