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:
f(x) = 29
Step-by-step explanation:
f(x)=23-(3x0)-(2X0)+6
f(x)=23+6
f(x)=29
The answer is: " 1 " .
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Explanation:
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7⁶ * 7⁻⁶ = 7⁽⁶⁺⁽⁻⁶⁾⁾ = 7⁽⁶⁻⁶⁾ = 7⁰ = 1 . The answer is: "1" .
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Note the following properties of exponents:
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1) xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ ;
2) x⁰ = 1 ; (x ≠ 0) ;
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Answer:
3840
Step-by-step explanation:
Hope this helps you out
Use the formula given to you with the triangle and the two numbers that are in the triangle.
