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Please help me with my Trigonometry?
1.[√5(cos(5π/16))+isin(5π/16)]^4
2. [^3√7(cos(π/18))+isin(π/18)]^6
2 Answers
- King LeoLv 72 years agoFavorite Answer
.
De Moivre’s Theorem: if z = r ( cos𝚹 + isin𝚹 ) then zⁿ = rⁿ ( cos(n𝚹) + isin(n𝚹) )
( 1 )
( √5 [ cos(5π/16) + isin(5π/16) ] )⁴
= ( √5 )⁴ [ cos(4 * 5π/16) + isin(4 * 5π/16) ]
= 25 [ cos(5π/4) + isin(5π/4) ]
= 25 ( -½√2 - ½i√2 )
= -25/2 ( √2 + i√2 )
━━━━━━━━━
( 2 )
[∛7 ( cos(π/18) ) + isin(π/18) ]⁶
= [ (∛7)⁶ ( cos(6 * π/18) ) + isin(6 * π/18) ]
= [ (7)² ( cos(⅓π) ) + isin(⅓π) ]
= 49 ( ½ + ½i√3 )
━━━━━━━━
- az_lenderLv 72 years ago
#1.
25[cos(5pi/4) + i*sin(5pi/4)]
= 25[-sqrt(2)/2 - i*sqrt(2)/2]
= -12.5*sqrt(2)*(1+i).
#2.
49*[cos(pi/3) + i*sin(pi/3)]
= 24.5*[1 + i*sqrt(3)]
