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
Answer:
The answer is B
Step-by-step explanation:
You need to graph the equation from the left of equality sign which is y=x*1/6 and the other is -2x+5
The first has a point (0,0) and other point could be (6,1) from there you can have your graph
The second has one point in (2.5, 0) and (0,5)
2835 divided by 5 equals 567.
The answer is d because it cannot be factored
