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What is the conjugate of the given complex number?z = 3i + 7
Question

What is the conjugate of the given complex number?

z = 3i + 7

A.

z=3+7i\overline{\mathrm{z}}=3+7 \mathrm{i}​​

B.

z=3i+7\overline{\mathrm{z}}=-3\mathrm{i}+7​​

C.

z=3i7\overline{\mathrm{z}}=3\mathrm{i}-7​​

D.

z=3i7\overline{\mathrm{z}}=-3\mathrm{i}-7​​

Correct option is B

The conjugate of a complex number z=a+bi is denoted as z and is defined as:z=abiHere, the real part (a) remains the same, while the imaginary part (b) changes sign.Given:z=7+3i Real part (a)=7 Imaginary part (b)=3The conjugate is:z=73i\begin{aligned}&\text{The conjugate of a complex number } z = a + bi \text{ is denoted as } \overline{z} \text{ and is defined as:} \\&\overline{z} = a - bi \\[10pt]&\text{Here, the \textbf{real part} } (a) \text{ remains the same, while the \textbf{imaginary part} } (b) \text{ changes sign.} \\[15pt]&\text{Given:} \\&\qquad z = 7 + 3i \\[5pt]&\bullet\ \text{Real part } (a) = 7 \\&\bullet\ \text{Imaginary part } (b) = 3 \\[5pt]&\text{The conjugate is:} \\&\qquad \overline{z} = 7 - 3i\end{aligned}​​

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