CVP1

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Show that \overline {z_{1}+z_{2}}=\overline {z_{1}}+\overline {z_{2}}\,.

Let z_{1}=x_{1}+iy_{1}\, and z_{2}=x_{2}+iy_{2}\,.

=\overline {x_{1}+iy_{1}+x_{2}+iy_{2}}=\overline {x_{1}+x_{2}+i(y_{1}+y_{2})}\,

=x_{1}+x_{2}-i(y_{1}+y_{2})=x_{1}-iy_{1}+x_{2}-iy_{2}\,

=\overline {x_{1}+iy_{1}}+\overline {x_{2}+iy_{2}}=\overline {z_{1}}+\overline {z_{2}}\,

Complex Variables

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