Which of the following complex numbers lies on the unit circle?

Which of the following complex numbers lies on the unit circle?

Step 1: Understand that a complex number is in the form z = a + bi, where a is the real part and b is the imaginary part.
Step 2: Know that the unit circle is defined as the set of complex numbers where the distance from the origin (0,0) is 1.
Step 3: The distance (or modulus) of a complex number z = a + bi is calculated using the formula |z| = √(a² + b²).
Step 4: To check if a complex number lies on the unit circle, we need to see if |z| equals 1.
Step 5: For the complex number z = 1 + 0i, calculate |z|: |z| = √(1² + 0²) = √(1) = 1.
Step 6: For the complex number z = 0 + 1i, calculate |z|: |z| = √(0² + 1²) = √(1) = 1.
Step 7: Since both calculations give us 1, we conclude that both 1 + 0i and 0 + 1i lie on the unit circle.

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