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Let = r, (cos 0, + isin 0, ) and r, (cos 0, + i sin 0, ). Z, = X1 + iy, 1 Z 2 X2 + iy, Then show that (i): r," .r," (cos n (0, + 0, ) + i sin n (0, + 0 , )) n z"1.Z 1 1 (ii): (cosn (0, - 0, ) + i sin n (0, - 0, )) %3D 2 n 2

Let = r, (cos 0, + isin 0, ) and r, (cos 0, + i sin 0, ). Z, = X1 + iy, 1 Z 2 X2 + iy, Then show that (i): r," .r," (cos n (0, + 0, ) + i sin n (0, + 0 , )) n z"1.Z 1 1 (ii): (cosn (0, - 0, ) + i sin n (0, - 0, )) %3D 2 n 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let z, = x, + iy, = , (cos 0, + i sin 0,) and Z1 1 1 1 z, = x, + iy, = r, (cos 0, r2 (cos 0, + i sin 0, ). Z 2 2 Then show that (i): n Z 2 ," .r," (cos n (0, + 0, ) + i sin n (0, + 0,)) 1. 1 n (ii): (cosn (0, 0,)+ i sin n (0, - 0 2 )) 1 1 n 2
Transcribed Image Text:Let z, = x, + iy, = , (cos 0, + i sin 0,) and Z1 1 1 1 z, = x, + iy, = r, (cos 0, r2 (cos 0, + i sin 0, ). Z 2 2 Then show that (i): n Z 2 ," .r," (cos n (0, + 0, ) + i sin n (0, + 0,)) 1. 1 n (ii): (cosn (0, 0,)+ i sin n (0, - 0 2 )) 1 1 n 2
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