Using <span>De Moivre's formula
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if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
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Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
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The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
Option ( C ) is the correct answer.
Answer:
the answer is 92.
Step-by-step explanation:
do 28 times 4, 28 for the days and 4 for the total laps each day.
Answer:
b=3g-5
Step-by-step explanation:
3 times Gracie's age = 3g
Ben is 5 years less = -5
3g-5=Ben
Ben=3g-5
Hope this helped! :^)
Change all mixed fractions to improper fractions.
1 2/7 = 7/7 + 2/7 = 9/7.
Subtract
9/7 - 6/7 = 3/7
3/7 is your answer
Hope this helps
