$z=-12 i+11$ $\newline$ What are the real and imaginary parts of $z$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $\begin{array}{l} \operatorname{Re}(z)=11 \text { and } \\ \operatorname{Im}(z)=-12 \end{array}$ $\newline$ (B) $\newline$ $\begin{array}{l} \operatorname{Re}(z)=11 \text { and } \\ \operatorname{Im}(z)=-12 i \end{array}$ $\newline$ (C) $\newline$ $\begin{array}{l} \operatorname{Re}(z)=-12 i \text { and } \\ \operatorname{Im}(z)=11 \end{array}$ $\newline$ (D) $\newline$ $\begin{array}{l} \operatorname{Re}(z)=-12 \text { and } \\ \operatorname{Im}(z)=11 \end{array}$

Full solution

z=-12 i+11

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What are the real and imaginary parts of

z

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Choose

1

answer:

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(A)

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\begin{array}{l} \operatorname{Re}(z)=11 \text { and } \\ \operatorname{Im}(z)=-12 \end{array}

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(B)

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\begin{array}{l} \operatorname{Re}(z)=11 \text { and } \\ \operatorname{Im}(z)=-12 i \end{array}

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(C)

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\begin{array}{l} \operatorname{Re}(z)=-12 i \text { and } \\ \operatorname{Im}(z)=11 \end{array}

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(D)

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\begin{array}{l} \operatorname{Re}(z)=-12 \text { and } \\ \operatorname{Im}(z)=11 \end{array}

Identifying the Complex Number: The complex number is given as $z = -12i + 11$ . To find the real and imaginary parts of $z$ , we need to identify the terms without the imaginary unit $i$ as the real part, and the terms with the imaginary unit $i$ as the imaginary part.
Finding the Real Part: The real part of the complex number $z$ is the term without the imaginary unit $i$ , which is $11$ . Therefore, $\text{Re}(z) = 11$ .
Finding the Imaginary Part: The imaginary part of the complex number $z$ is the term with the imaginary unit $i$ , which is $-12i$ . However, when we refer to the imaginary part, we only take the coefficient of $i$ , which is $-12$ . Therefore, $\text{Im}(z) = -12$ .
Matching with Given Choices: Now we can match our findings with the given choices. The correct choice should have $\text{Re}(z) = 11$ and $\text{Im}(z) = -12$ .
Correct Choice: Looking at the choices, we see that option (A) matches our findings: $\text{Re}(z) = 11$ and $\text{Im}(z) = -12$ .