If z1-z2 are complex numbers- then the maximum value of z1z-2-z-1-z2-z1z2-z-1-z-2-z1z2- is equal to

Z_1=r_1e^iθ_1, z_2=r_2e^iθ_2 ⇒z_1z̅_̅2̅+z̅_̅1̅z_2+z_1z_2+z̅_̅1̅z̅_̅2̅/|z_1z_2|=2 cos(θ_1 θ_2)+2cos(θ_1+θ_2)≤4 nbsp; ...

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Euler's Representation

If z1,z2 are ...

Question

If $z_{1}, z_{2}$ are complex numbers, then the maximum value of $\frac{z_{1}_{2} +_{1} z_{2} + z_{1} z_{2} +_{1}_{2}}{| z_{1} z_{2} |}$ is equal to

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z_{1}

z_{2}

u = \sqrt{z_{1} z_{2}},

∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} + u ∣ ∣ ∣ + ∣ ∣ ∣ \frac{z_{1} + z_{2}}{2} - u ∣ ∣ ∣

Z_{1}, Z_{2}

Z_{1} + Z_{2}, Z_{1} Z_{2}

z_{1}, z_{2}

| z_{1} | = | z_{2} | = 2

arg z_{1} + arg z_{2} = 0

z_{1} z_{2} =

z_{1}, z_{2}

| z_{1} | = | z_{2} | = 2

arg z_{1} + arg z_{2} = 0

z_{1} z_{2} =

∣ ∣ ∣ \frac{_{1} - 2_{2}}{2 - z_{1}_{2}} ∣ ∣ ∣ = 1

| z_{2} | \neq 1,

z_{1}

z_{2}

| z_{1} |

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