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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)
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Find log(5 + 12i)
Find 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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Description
This quiz focuses on various topics in complex analysis, including simplification of expressions, solving polynomial equations, and separating functions into their real and imaginary parts. Additionally, it covers the representation of trigonometric functions in terms of powers and logarithmic calculations involving complex numbers.
