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- Let a = V3 – i and b = –1+ i be two complex numbers. (9a) Compute the value of b18 Z = a7 (9b) Find all solutions w to the equation w³ 462. (Note: the final answers to 9a and 9b should be given in the standard form x + iy).arrow_forwardTake the last four digits ABCD of your student identification number, andlet z1= A + Bi and z2 = C + Di be the corresponding complex numbersobtained as indicated. Find the complex number z = p + qi such that (1/z)=(1/z1)+(1/z2) In the second problem you should compute p and q explicitly to four significant digits. My last four digits: 0564arrow_forwardSuppose z0 is any constant complex number on the interior of any closed simple curve. of the contour C. Show that for a positive integer n :arrow_forward
- 2. Evaluate the following. Express all answers in rectangular form. Solutions for complex number transformation are not required in these items. c. (√(2+i)²arrow_forwardI. X D f(z) is equal to the above Let z be a non-zero complex number. Then Log(z²) = 2Logz if -TTSArg(z)s0 if OsArg(z)e for all complex numbers z. Then f is an exponentia' ction such a function does not existarrow_forward3. Consider f(2)=(+)1/3. Choose a set of branch cut (s) and sketch it in the complex plane. For this choice, derive the branch functions f..(2).arrow_forward
- Given the complex numbers z, = 2+ j0.51, zz = -0.4- j0.8, and z3 = 3+j3 find; |21Z2 (Z – 23) + Im(zz + z1)| In decimal form: z = x + jy Re(z)+ )Im(z) %3Darrow_forwardConsider the complex-valued function f (x + iy) = x² + ay² – 2xy + i(bx – y² + 2xy). Find values of a and b Correct answers are integers. No spaces, no punctuation except for minus signs if necessary. so that f (x +iy) will be analytic. a= type your answer... and b = type your answer...arrow_forward4. Consider the complex number w = 3cis (). For which value(s) of k is z- w a factor of the polynomial f(z) = r³ – k?arrow_forward
- For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find æ, Y, r, 0 in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number. 1. 1+i 2. i - 1 3. 1- iv3 4. -v3+i 5. 2i 6. -4i 7. -1 8. 3 9. 2i – 2 10. 2 – 2i 11. 2 ( cos +i sin 2т 37 12. 4 i sin 13. + i sin COS Cos 2 2 14. 2 (cos + 2 ( cos 15. COS IT i sin 7 16. 5(cos 0 + i sin 0) Vze-iz/4 17. 18. 3e/2 19. 5(cos 20° + i sin 20°) 20. 7(cos 110° – i sin 110°)arrow_forwardIf zz = -4 + j5, z2 = 3 - j2 , and z3 = 2 - j3 , what is Im (z; - 21) + 2; ? Note: 2* is the complex conjugate of z. Im (z) is the imaginary part of z O 1+ j2 O 11 + j2 none of the choices O -5+ j2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage