Question

[z₂ = 2 - i, quad x₂ = 2, quad y₂ = -1 → r² = 5, quad sin(θ) = -1/√5, quad θ₂ = -26]

[z₂/z₁ = (2.5)^0.5 ⋅ (cos(-71) + isin(-71))]

a) ((2.5)^0.5 ⋅ (cos(-71) + isin(-71)))

b) ((2.5)^0.5 ⋅ (cos(71) + isin(71)))

c) ((2.5)^0.5 ⋅ (cos(-26) + isin(-26)))

d) ((2.5)^0.5 ⋅ (cos(26) + isin(26)))

Answer 1

The correct representation of the complex number is the polar form involving the magnitude √2.5 and the trigonometric functions of the angle, which should be appropriately signed based on the trigonometric identities.

Step-by-step explanation:

The student is asking about the complex division of two complex numbers and how to represent the result in polar form. The correct polar representation would involve the magnitude √2.5 (square root of 2.5) and the angle in degrees. The angle should preserve the original sign from the equation. As the provided angles are -71 and -26 degrees, we should consider the values of cosine and sine for those angles. Using standard trigonometric identities and properties, cos(-θ) = cos(θ) and sin(-θ) = -sin(θ), we can rewrite the answer with a positive angle where needed.