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Advanced Calculus and Complex Analysis: Analytic Functions

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Advanced Calculus and Complex Analysis: Analytic Functions

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Questions and Answers

What is the effect of the transformation W = AZ, where A ≠ 0, on the vector Z?

It rotates the vector Z by an angle |A| and scales its length by a factor of Α
It rotates the vector Z by an angle |A| and translates its length by a factor of Α
It rotates the vector Z by an angle Α and translates its length by a factor of |A|
It rotates the vector Z by an angle Α and scales its length by a factor of |A| (correct)

What is the result of equating real and imaginary parts in the transformation W = Z + 2 - I?

U = X + 2 and V = Y - 1 (correct)
U = X - 2 and V = Y + 1
U = X - 2 and V = Y - 1
U = X + 2 and V = Y + 1

What is the region in the W-plane corresponding to the triangular region bounded by X = 0, Y = 0, X + Y = 3 under the transformation W = 2Z?

A 2-times magnified triangle (correct)
A 6-times magnified triangle
A 4-times magnified triangle
A 3-times magnified triangle

What is the transformation W = EIΠ/4 Z equivalent to?

A rotation of Π/4 radians (D) Signup and view all the answers

What is the region in the W-plane corresponding to the triangular region bounded by X = 0, Y = 0, X + Y = 1 under the transformation W = EIΠ/4 Z?

A region bounded by U = -V, U = V, and U + V = 1 (D) Signup and view all the answers

What is the transformation W = 2Z equivalent to?

A magnification of 2 times (D) Signup and view all the answers

What is the purpose of equating real and imaginary parts in the transformation W = Z + 2 - I?

To separate the real and imaginary components of the transformation (C) Signup and view all the answers

What is the effect of the transformation W = EIΠ/4 Z on the vector Z?

It rotates the vector Z by an angle of Π/4 radians (D) Signup and view all the answers

What is the transformation W = Z + 2 - I equivalent to?

A translation of 2 units and a rotation of Π/4 radians (C) Signup and view all the answers

What is the region in the Z-plane corresponding to the triangular region bounded by U = 0, V = 0, U + V = 6 under the transformation W = 2Z?

A triangle bounded by X = 0, Y = 0, X + Y = 3 (D) Signup and view all the answers