For z = a + bi, what are Re(z) and Im(z)?

For z = a + bi, what are Re(z) and Im(z)?

• A. Re(z) = a, Im(z) = b
• B. Re(z) = a, Im(z) = -b
• C. Re(z) = b, Im(z) = a
• D. Re(z) = -a, Im(z) = -b

Answer: (A)

The real part of a complex number is the coefficient of 1, and the imaginary part is the coefficient of i. For z = a + bi, where a and b are real numbers, the real part is a and the imaginary part is b. This matches the standard representation of a complex number as a point (a, b) in the Argand plane. So Re(z) = a and Im(z) = b. The other forms would correspond to different expressions, such as a − bi or −a, which aren’t what z = a + bi represents.

The real part of a complex number is the coefficient of 1, and the imaginary part is the coefficient of i. For z = a + bi, where a and b are real numbers, the real part is a and the imaginary part is b. This matches the standard representation of a complex number as a point (a, b) in the Argand plane. So Re(z) = a and Im(z) = b. The other forms would correspond to different expressions, such as a − bi or −a, which aren’t what z = a + bi represents.