For each of the following complex number(s), perform the following operations and express the results in...
Plot the complex number. Then write the complex number in polar form. Express the argument as an angle between 0 degrees and 360 degrees . 1-4i z=___(cos__+i sin__)
Question 1: Plot the complex number. Then write the complex number in polar form. Express the argument as an angle between 0 and 360° 2+4 i Almaginary Plot the complex number. OS - z= (cos + i sin D) Type an exact answer in the first answer box. Type all degree measures rounded to one decimal place as needed.)
III) Perform the following complex number conversions (a) convert the complex number Zi- 3+j4 to polar form tb) convert the complex number Z2-4 e0 to polar and rectangular form Hint: Z2-rexponential form. form IV What are the phase relationship between the sinusoidal waveforms brelow: v=4sin (wt + 50) i 6 sin (wt + 40) (b) v 2 cos (wt 30) i 5 sin (wt60)
Question 3.1 (10 marks) Consider the two complex numbers-V3+i and 2 3 cis(-/3) a) Write 1V3+i in polar form, in terms of its principal argument. b) Use your answer in a) to evaluate z1/21 in polar form, and then convert that into cartesian form. c) Using their polar forms, determine z122 and z2/句in terms of their principal argument. d) Determine (22)2 in polar form, in terms of its principal argument. e) Determine all distinct values of (22)1/3 in polar form,...
3. Perform the following complex number calculations (Note: Electrical engineers use j Express your answer in rectangular and polar format (3 +j4) + (4-J2)- (3 +j4)-(4-J2)- (3 +/4) * (4-y2) = (3 +j4)/ (4-j2)- instead of i for the imaginary component) (rectangular) (rectangular) (rectangular) (rectangular) (polar) (polar) (polar) (polar)
Nrite the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. -5-51 O A. 542(cos 225° + i sin 225º) O B. 25( cos 225° + i sin 225°) OC. 25(cos 230° + i sin 230°) OD. 572(cos 230° + i sin 230°)
Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 3-3i O A. 9( cos 300° + i sin 300°) OB. 9( cos 315º + i sin 315º) O C. 313(cos 315º + i sin 315º) OD. 343( cos 300° + i sin 300°)
2. (a) Express each of the following complex numbers in polar form (i) i ( ii) /3 - 3i (iii) -3-V3i 42 b) For each of the complex numbers in part (a), id and
#1,5,9 and #13,17,21,25 please. In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
The polar form of a complex number z = a+bi is z = r(cosθ+isinθ) , where r = |z| = sqrt(a^2+b^2) , a = rcosθ and b = rsinθ and θ = tan^−1(b/a) for a > 0 and θ = tan^−1(b/a ) + π or θ = tan^−1(b/a) +180° for a < 0. What is the value for θ = tan^−1(b/a) for a = 0? Example: Express z = 0 + i in polar from with the principal argument. The...