Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 20.2, Problem 5E
To determine
To find: Where the given complex mapping is conformal.
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2. Show that for any x, the matrix A =
A² = I.
[cos(2x)
sin(2x)
sin(2x)
cos(2x)
satisfies the relation
In Problems 31–34, find the complex zeros of each polynomial function f1x). Write f in factored form.
Problem 4: Consider the set of polynomials {2+t, 1 – 5t}. Let p,(t) = 2 + t and
P2(t) = 1 – 5t. Let B = {2+t, 1 – 5t}.
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- 3. Consider the linear transformations T : R² → R² and S: R? → R² defined by 7 (E)-E :(E)-L] [2x2 X2 T S 3x2] X1 Find T-1 and S-'. Using your answers, write a formula for (TS)-1.arrow_forwardQ6. (a) i. Determine the bilinear transformation that maps the points 1 – 2i, 2 + i 2 + 3i respectively into 2 + 2i, 1+ 3i, 4. 1-i ii. Evaluate f 4z dz . 3i ez (b) Evaluate J. dz, where C: |z| = 3. (z-1)(z-2)2arrow_forward3. Explain why whenever A is a Ax = 0 always has linear transformation, solutionarrow_forward
- 2) The complex conjugate of z is denoted as z. Solve for z in the equation: Z – 12 = j(9 – 27) - giving the answer in the form x + jy, where x and y are real numbers.arrow_forward3. Consider the linear transformations T: R² → R² and S: R² → R² defined by X1 X1 X2 ([2₂]) S ([21]) = [₁ ² ³37 X2 x1 - 3x2 T 2x2 3x1 1 Find T-¹ and S-1. Using your answers, write a formula for (TS)-¹.arrow_forwardExample 23: Show that, if Y (t) = X (t + a) –X (t - a), then, (i) Ryy (t) = 2 Rxx (t) – Rxx (T + 2a) – Rxx (t - 2a) andarrow_forward
- how do i find the xx- and yy-components of B⃗ B→ in the coordinate system shown in (Figure 1)arrow_forward#2. Find the Jacobian of the transformation x = 2uv + 3 y = vw Z = wu.arrow_forward. Let L : R³ → R₂[x] be a linear transformation such that L ¹() L (:) (a) −3+2x6x² = -1. Which of the following equals L2 ? ² (:-) ₂ 3 (b) 3-2x6x² (c)-3-2x + 6x² ¹ (0) = 2x, L1 = -3x² and (d)-3-2x6x²arrow_forward
- 1. Determine whether the following pairs of operators commute d (a) (b) dx хarrow_forwardQ1. Let f(z)=y– 2xy+i(-x+x² – y²)+z² where, z=x+iy is a complex variable defined in the whole complex plane. For what values of z does f'(z) exist?arrow_forward17. Calculate the real values of m such that the following conic section is degenerated x² - 4xy + 2y²-5y-m x + 2 = 0. Ans. m +- 3/2 (2)^1/2-5arrow_forward
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