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Question : 10 of 160
Marks:
+1,
-0
Solution:
‌eiθ=cis‌θ=cos‌θ+isin‌θ‌‌‌=Re[‌]‌=Re[(‌)n]‌ [Using De-moivre theorem] ‌‌=Re[(‌)n]=Re[1+‌+(‌)2+...∞]1+‌+(‌)2+...... is an GP
=Re[‌]=Re[‌]‌=Re[‌| 2 |
| 2−cos‌θ−isin‌θ |
]‌=Re[‌| 2(2−cos‌θ−isin‌θ) |
| (2−cos‌θ)2−i2sin‌2θ |
]‌=Re[‌| 4−2‌cos‌θ |
| 4+cos2θ−4‌cos‌θ+sin‌2θ |
.‌=‌| isin‌θ |
| 4+cos2θ−4‌cos‌θ+sin‌2θ |
]‌=‌| 4−2‌cos‌θ |
| 5−4‌cos‌θ |
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