Verify the following- - z1 - z2-2 - - z 1pt 1-2 - - z2-2 - 2 Re z1z2

LHS=|z_1 z_2|^2=|z_1 z_2||z̅_̅1̅ z̅_̅2̅| =z_1z̅_̅1̅+z_2z̅_̅2̅ z_1z̅_̅2̅ z_2z̅_̅1̅ =|z_1|^2+|z_2|^2 2Re(z_1z̅_̅2̅) =RHS ...

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Modulus of a Complex Number

Verify the fo...

Question

Verify the following:
${| z_{1} - z_{2} |}^{2} = {| z_{1} |}^{2} + {| z_{2} |}^{2} - 2 Re (z_{1} ¯ ¯¯¯ ¯ z_{2})$

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If arg ( $Z_{1}$ ) = $α$ , arg ( $Z_{2}$ ) = $β$ , the value of $| Z_{1} + Z_{2} |^{2}$ is

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| z_{1} | + | z_{2} | = ∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} + \sqrt{z_{1} z_{2}} ∣ ∣ ∣ + ∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} - \sqrt{z_{1} z_{2}} ∣ ∣ ∣

{| z_{1} + z_{2} |}_{1}^{2} = {| z_{1} |}_{1}^{2} + {| z_{2} |}_{2}^{2}

| z_{1} |, | z_{2} | \neq 0

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| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2} = 2 (| z_{1} |^{2} + | z_{2} |^{2})

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z_{2} .

z_{1}, z_{2}, ε C

| z_{1} + z_{2} |^{2} = | z_{1} |^{2} + | z_{2} |^{2}

\frac{z_{1}}{z_{2}}

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