10 Questions
What is the effect of the transformation W = AZ, where A ≠ 0, on the vector Z?
It rotates the vector Z by an angle Α and scales its length by a factor of |A|
What is the result of equating real and imaginary parts in the transformation W = Z + 2 - I?
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
What is the transformation W = EIΠ/4 Z equivalent to?
A rotation of Π/4 radians
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
What is the transformation W = 2Z equivalent to?
A magnification of 2 times
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
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
What is the transformation W = Z + 2 - I equivalent to?
A translation of 2 units and a rotation of Π/4 radians
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
Test your knowledge of analytic functions, including their definition, properties, and determination of harmonic conjugate. Learn about Cauchy-Riemann equations and Milne-Thomson's method. This quiz covers advanced calculus and complex analysis topics.
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