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P Suppose z = x + iy and w = u + iv. a) Prove that z+w = z+ w (i.e., the conjugate of the sum is equal to the sum of the conjugates) b) Prove that Re(z + w) = Re(z) + Re(w) (i.e., the real part of the sum is equal to the sum of the real parts) C. c) Is it true that Re(z x w) = Re(z) x Re(w)? Verify that z = 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2 + 41 also a solution? Does your answer contradict Euler's 1742 observation that solutions to polynomial equations with real coefficients come in conjugate pairs? 72 F Clear 近 0 図 prt sc delete insert f12 LLJ VI 64 OLI 因ッ backspace [ K H. 7.

P Suppose z = x + iy and w = u + iv. a) Prove that z+w = z+ w (i.e., the conjugate of the sum is equal to the sum of the conjugates) b) Prove that Re(z + w) = Re(z) + Re(w) (i.e., the real part of the sum is equal to the sum of the real parts) C. c) Is it true that Re(z x w) = Re(z) x Re(w)? Verify that z = 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2 + 41 also a solution? Does your answer contradict Euler's 1742 observation that solutions to polynomial equations with real coefficients come in conjugate pairs? 72 F Clear 近 0 図 prt sc delete insert f12 LLJ VI 64 OLI 因ッ backspace [ K H. 7.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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P Suppose z = x + iy and w = u + iv. a) Prove that z+w = z+ w (i.e., the conjugate of the sum is equal to the sum of the conjugates) b) Prove that Re(z + w) = Re(z) + Re(w) (i.e., the real part of the sum is equal to the sum of the real parts) C. c) Is it true that Re(z x w) = Re(z) x Re(w)? Verify that z = 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2 + 41 also a solution? Does your answer contradict Euler's 1742 observation that solutions to polynomial equations with real coefficients come in conjugate pairs? 72 F Clear 近 0 図 prt sc delete insert f12 LLJ VI 64 OLI 因ッ backspace [ K H. 7.
Transcribed Image Text:P Suppose z = x + iy and w = u + iv. a) Prove that z+w = z+ w (i.e., the conjugate of the sum is equal to the sum of the conjugates) b) Prove that Re(z + w) = Re(z) + Re(w) (i.e., the real part of the sum is equal to the sum of the real parts) C. c) Is it true that Re(z x w) = Re(z) x Re(w)? Verify that z = 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2 + 41 also a solution? Does your answer contradict Euler's 1742 observation that solutions to polynomial equations with real coefficients come in conjugate pairs? 72 F Clear 近 0 図 prt sc delete insert f12 LLJ VI 64 OLI 因ッ backspace [ K H. 7.
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