7. If aatiß = (x + iyy*4, a>0, prove that %3D (i) a = 5 log, (x + y) -q tan log, e- loga (r + y) = 2(ap + Bq) p* + q* (ii)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Prove the expressions

7.
If aa+iß = (x+ iyy+i4, a> 0, prove that
%3D
1
(i)
= ; loga (x + y) - q tan
| loga e.
(ii) log, G + y°) = 2(ap+ a)
p + q
Transcribed Image Text:7. If aa+iß = (x+ iyy+i4, a> 0, prove that %3D 1 (i) = ; loga (x + y) - q tan | loga e. (ii) log, G + y°) = 2(ap+ a) p + q
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The given isaα+iβ=x+iyp+iq,a>0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

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