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Find the complex conjugate bar(z_(1)) of {:[z_(1)=-4i+4.],[ bar(z_(1))=◻]:}

Find the complex conjugate z1‾ \overline{z_{1}} of\newlinez1=−4i+4z1‾=□ \begin{array}{l} z_{1}=-4 i+4 \\ \overline{z_{1}}=\square \end{array}

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Full solution

Q. Find the complex conjugate z1‾ \overline{z_{1}} of\newlinez1=−4i+4z1‾=□ \begin{array}{l} z_{1}=-4 i+4 \\ \overline{z_{1}}=\square \end{array}
  1. Identify Parts of z1z_1: Identify the real and imaginary parts of the complex number z1z_1. In z1=−4i+4z_1 = -4i + 4, the real part is 44 and the imaginary part is −4-4 (the coefficient of ii). Real part: 44 Imaginary part: −4-4
  2. Find Complex Conjugate: Determine the complex conjugate of z1=−4i+4z_1 = -4i + 4. The complex conjugate of a complex number is obtained by changing the sign of the imaginary part. Therefore, the complex conjugate of −4i+4-4i + 4, denoted as z1ˉ\bar{z_1}, is 4i+44i + 4. Complex conjugate: z1ˉ=4i+4\bar{z_1} = 4i + 4

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