Question

parts of complex numbers
google classroom microsoft teams
$z = 44i - 32$
what are the real and imaginary parts of $z$?
choose 1 answer:
a $\text{re}(z) = 44i$ and $\text{im}(z) = -32$
b $\text{re}(z) = -32$ and $\text{im}(z) = 44$
c $\text{re}(z) = -32$ and $\text{im}(z) = 44i$
d $\text{re}(z) = 44$ and $\text{im}(z) = -32$

Explanation:

Step1: Recall complex number form

A complex number \( z \) is written as \( z = a + bi \), where \( a \) is the real part (\( \text{Re}(z) \)) and \( b \) is the imaginary part (\( \text{Im}(z) \)) (without the \( i \)).

Step2: Rewrite given \( z \)

Given \( z = 44i - 32 \), we can rewrite it as \( z = -32 + 44i \).

Step3: Identify real and imaginary parts

Comparing with \( z = a + bi \), we have \( a = -32 \) (real part) and \( b = 44 \) (imaginary part, since the imaginary part is the coefficient of \( i \), not including \( i \) itself).

Answer:

B. \( \text{Re}(z) = -32 \) and \( \text{Im}(z) = 44 \)