Question

What are the real and imaginary parts of the complex number z = 21 + 13i?

A) Re(z) = 21, Im(z) = 13
B) Re(z) = 21, Im(z) = i
C) Re(2) = i, Im(z) = -13
D) No correct option provided

Answer 1

The real and imaginary parts of the complex number z = 21 + 13i are Re(z) = 21 and Im(z) = 13, respectively.

Step-by-step explanation:

The real and imaginary parts of a complex number are denoted by Re(z) for the real part and Im(z) for the imaginary part. Given a complex number z = a + bi, where a is the real part and bi is the imaginary part, the real part is simply the coefficient in front of the real unit (1 or the absence of i), and the imaginary part is the coefficient in front of the imaginary unit (i).

For the complex number z = 21 + 13i, the real part is 21 and the imaginary part is the coefficient of i, which is 13. Therefore, the correct answer to what are the real and imaginary parts of the complex number z = 21 + 13i is Re(z) = 21, Im(z) = 13.