Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 . Computez1z2.
(a) 8(cos?π?+isin?π?) 22
(b) 4(cos?4π?+isin?4π?) 66
(c) 2(cos?π?+isin?π?) 66
(d) cos(π)+isin(π)
(e) 8(cos?π?+isin?π?)
66
Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 . Computez1z2. (a) 8(cos?π?+isin?π?)...
5 and 6
5. -/2.38 points Salg Trig4 8.T.005. Let Z1 = 2 ( cos(77) + i sin(79)) and 22 = 7(cos(54) + i sin(5). Find Z222 and 1(Enter your answers in a + bi form.) Z122 = 6. -/2.38 points SAlg Trig4 8.1.006. Find the cube roots of 1256. (Enter your answers as a comma separated list.) Sketch these roots in the complex plane.
Multiply. Leave the answer in trigonometric form. 4(cosi 15° +isin 115°) 6(cos56° +isin 56°) V T TT TT Paragraph Arial % DOO fx Mashup « 3 (12pt) T TO 1 HTML, CSS Path:p QUESTION 9 Find the quotient in standard form 2. - 12-121, 21-4-41 O. 3 Find the quotient 22 in standard form. 21 = 12–12i, 21 = 4-41 O a. 3 O b.31 Oc. -6 d 6 e. -3 QUESTION 10
Given 21 = -5(cos(127') + i sin(127)) 22 = 8(cos(8") + sin(8')) Find the product Z122. Provide your answer below:
8. Let w cos(2π/5) + isin(2π/5). Here we describe how to express w in terms of square roots. (a) Show that w is a root of the polynomial 24+2+22+21. Hint: 25-1-(-(24+23+22+2+1) (b) Show that w + is a root of the polynomial u2 + u-1 (c) Show that Ve, where V5 means the positive square root of Hint: Figure out the sign of w by adding the polar forms of w and 1/w. (d) Put β--12vS So in part (c),...
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+
40 Show the following results. 1-e2...
4. π a. The graph of y = cos x can be obtained by translating the graph of y = sin x rad to the right rad to the left rad to the right d. rad to the left 2 п 2 TT b. 4
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,...
- Problem 6. Consider the function y2 m) sin ((10/s) t+π/4). lndicate whether each of the following waveforms is equivalent to y? Briefly justify your answers 1. (2 m) cos(10/s)t+/4) 2. (2 m) cos( (10/s)t+3 T/4) 3. (2m) cos( (10/s)t -/4) 4. (2 m) sin((10/ s) t + π/4 + 4 π) 5.-(2 m) sin ((10/s) t + π /4-3r) 6. (-2m) cos((10/s) t + 12n/4) 7. (v ฐ m) [cos((10/s) t) + sin((10/s) t)] 8. (2 m) cos ((-10/s)...
Consider the function
f ( x ) = 4 π ( cos x 1 − cos 3 x 3 + cos 5 x 5 − cos 7 x 7
+ ⋯ ). Fire up a plotting program or spreadsheet, and plot this
over the range of x=0 to 4π. Do it one term at a time, so make four
plots: one with the first term, one with the first and second, the
next with one, two,...
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e
Define f: R2R3 b f(s,t) (sin(s) cos(t),...