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Questions and Answers
Simplify: (cosθ + isinθ)^-6(cos4θ + isin4θ)^-2 / (cos6θ - isin6θ)^2 (cos3θ + isin3θ)^6
Simplify: (cosθ + isinθ)^-6(cos4θ + isin4θ)^-2 / (cos6θ - isin6θ)^2 (cos3θ + isin3θ)^6
1
Solve: x^5 - 1 = 0
Solve: x^5 - 1 = 0
x = 1, -1, (1/2) + (√3 / 2)i, (1/2) - (√3 / 2)i, -1
Express sin60 and cos60 in powers of sin θ.
Express sin60 and cos60 in powers of sin θ.
sin60 = (√3 / 2) = √(1 - (1 / 4)) = √((4 - 1) / 4) = √3 / 2, cos60 = (1 / 2) = (1 - sin^2(60))^1/2
Separate the following functions into real and imaginary parts: i) sin(x - iy), ii) cos(x - iy)
Separate the following functions into real and imaginary parts: i) sin(x - iy), ii) cos(x - iy)
Find log(5 + 12i)
Find log(5 + 12i)
Flashcards
Simplifying complex exponentials
Simplifying complex exponentials
Using De Moivre's theorem to simplify expressions involving powers of complex numbers in trigonometric form.
Solving $x^5 - 1 = 0$
Solving $x^5 - 1 = 0$
Finding the roots (solutions) of a polynomial equation.
Expressing $\sin60^\circ$ and $\cos60^\circ$
Expressing $\sin60^\circ$ and $\cos60^\circ$
Writing $\sin60^\circ$ and $\cos60^\circ$ in terms of $\sin heta$ and $\cos heta$ for a general angle $ heta$.
Separate $\sin(x-iy)$ into real and imaginary parts
Separate $\sin(x-iy)$ into real and imaginary parts
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Separate $\cos(x-iy)$ into real and imaginary parts
Separate $\cos(x-iy)$ into real and imaginary parts
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Calculate $\log(5+12i)$
Calculate $\log(5+12i)$
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Study Notes
Assignment - 03
- Simplify: (cos60 + isin60)² (cos40 - isin40)² / (cos60 - isin60)² (cos30 + isin30)⁶
- Solve x⁵ - 1 = 0
- Express sin60° and cos60° in terms of powers of sin and cos.
- Separate the following functions into real and imaginary parts:
- sin(x - iy)
- cos(x - iy)
- Find log(5 + 12i)
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