Could you explain how to show this in detail? Recall that the Euclidean scalar product in R² is defined by(x1, Y1) · (x2, Y2) := x1x2+ Y1 Y2 ·(i) Show that, setting z1 = x1+ iy1 and z2 = x2+ iy2, it holds21 · Z2 = Re (21z2).(ii) Show that, in the situation of Exercise 1 and with (1) enforced it holdsAz · Awforevery z, w E C\{0}.|Az||Aw||z||w|(Hint: Use (v) of Exercise 1). Discuss the geometric meaning of the above identity.

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Description: Could you explain how to show this in detail? Recall that the Euclidean scalar product in R² is defined by(x1, Y1) · (x2, Y2) := x1x2+ Y1 Y2 ·(i) Show that, setting z1 = x1+ iy1 and z2 = x2+ iy2, it holds21 · Z2 = Re (21z2).(ii) Show that, in the sit

Answered: Recall that the Euclidean scalar…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Could you explain how to show this in detail?

Recall that the Euclidean scalar product in R² is defined by
(x1, Y1) · (x2, Y2) := x1x2+ Y1 Y2 ·
(i) Show that, setting z1 = x1+ iy1 and z2 = x2+ iy2, it holds
21 · Z2 = Re (21z2).
(ii) Show that, in the situation of Exercise 1 and with (1) enforced it holds
Az · Aw
for
every z, w E C\{0}.
|Az||Aw|
|z||w|
(Hint: Use (v) of Exercise 1). Discuss the geometric meaning of the above identity.

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