If-z-1-2-and-z-2-2-Show-that-z-1-z-2-2-z-1-z-2-2-z-2-z-2-2-and-deduce-that-2-2-2-2-Thank-you-in-advan

Question Number 197851 by Mastermind last updated on 01/Oct/23

If z_{1} = \sqrt{\frac{α - β}{2}} and z_{2} = \sqrt{\frac{α + β}{2}} . Show

that ∣ z_{1} - z_{2} ∣^{2} + ∣ z_{1} + z_{2} ∣ = 2 ∣ z ∣^{2} + ∣ z_{2} ∣^{2} and

deduce that

∣ α + \sqrt{α^{2} - β^{2}} ∣ + ∣ α - \sqrt{α^{2} - β^{2}} ∣ = ∣ α + β ∣ + ∣ α - β ∣

Thank you in advance