Leabhar Iomlán - Cogg

7. cos i sin 8. (a) 8(cos i sin )(b) 16cos( ( ___ 2 3) i sin ( 16cos ___( 4 ___ 2 3)___3)3) i sin ( 4 9. (i)1_ (cos () i sin ())3(ii) 1_3 0i10. 4 ___(cos 2 3 i sin ___ 2 3)(a)z 2 16 ___(cos ( 4 3) i sin ___( 4 3)) 16 ___ 2(cos ( 3) i sin ( 8 8 √ __3 i)___ 2 3) )(b) z 3 64(cos (2) i sin (2)) 64 0i11. Cruthúnas12. ___ 1√ ___ 12 √ i213. CruthúnasCleachtadh 3.91. (i) 0 i (ii) √ _____ 32 1__2 i(iii) __ 12 ___ √__ 3i (iv) 1 0i2(iv) 1 0i(v) 0 i(vi) 1 0i(vii) 0 i(viii) 0 i2. 2, 2 √ __3 i3. 0 243i4. (i) cos ___ 2 3 i sin ___ 2 3(ii) cos ___ 2 3 i sin ___ 2 3 , __ 12 ___ √__ 32 i5. (i) 2 __(cos 6 i sin __ 6 )(ii) 3 ___(cos 2 3 i sin ___ 2 3)(iii) 2 __ (cos ( 6 ) i sin (__ (iv) 3 ___ 2(cos ( 3) i sin (6 ) )___ 2 3) )(v) 6 ___(cos 5 6 i sin ___ 5 6)(vi)2__ __ 3(cos ( 2 ) i sin __ ( 2 ))6. (i) 4 0i (ii) 8 0i (iii) 64 0i7. 48. 4 √ __ 2 __ (cos ( 4 ) i sin __(4 )) ; 19. (i) 1728 0i (ii) 409610. cos __ ( 6 ) i sin (11. 128 128 √ __3i__ 6 ) ; 1____256 ____ 1256 iCleachtadh 3.101. (i) 1 0i (ii) 1 0i(iii) 1 0i(iv) 1 0i2. (i) sin 2 2 sin cos (ii) cos 3 4 cos 3 3 cos 3. Cruthúnas4. 2, 1 √ __3 i, 1 √ __3 i5. 2, 1 √ __3 i, 1 √ __3 i6. 4 __(cos 3 i sin __ 3 ) ; √ __3 i, √ __3 i7. (a) (cos 2n i sin 2n), 1, __ 12 ___ √__ 32 i, __ 12 ___ √__ 32 i8. 3i, 3 √ ______ 32 __ 3 2 i, 3 √ ______ 32 __ 3 2 i√ __39. (i) ___√ 1__2 2 i, √ _____ 3√ 1__2 2 i(ii) √ __3 i, √ __3 i(iii) √ __2 √ __2 i, √ __2 √ __2 i10. cos ____( 2n 5) i sin ____( 2n 5),n {0, 1, 2, 3, 4}. CruthúnasSúil Siar (Croícheisteanna)1. 2 √ __52. x 5, y 43. 2 3i4. 24 10i, cruthúnas5. (i) 2 2 √ __3 i (ii) p 26. √ __2 __(cos 4 i sin __ 4 ) ; z4 4 0i7. 2 ___(cos 2 3 i sin ___ 2 3)8. 2 3i9. Tá10. 1 3i11. i12. f(z) z 2 (1 7i)z 14 5i13. (i) 1 2i (ii) 3 3i (iii) 2 5i14. (i) Rothlú (90°) agus ríochan de réirfachtóir 1 1 2(ii) An t-aistriú (4 i)(iii) Má tá z x iy, z 1 11_2 i(iv) z 3 (4 i)Súil Siar (Ardcheisteanna)1. x 4_ 5 52. 2 3i, 1_23. 2 __(cos 6 i sin __ 6 ) ; 210 ( √ __3 i)4. p 5 4i, q 1 7i288