Find all the values of (1 + 2i)1/3
Find all the values of (1 + 2i)}.
complex analysis 2. Find the absolute values of - 2i(3 + 1)(2+41) (1 + 1) and and (3 + 4i)(-1 + 21) (-1 - 0) (3 - 1)
3. Compute all possible values of i', log (-1 + V3i), sin(+ 2i). (Write your answers in the usual a + bi form.)
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
wnch S puytes to 3 2. Prove by induction on n that Li-1 (2i-1) (2i+1) 1 for n 1,2, 3, .... 2n+1
2i (a) Find where M(v) - ( b) Find M() for v 2z? + 2-1-5. - 2i (a) Find where M(v) - ( b) Find M() for v 2z? + 2-1-5. -
Find all solutions of 24 = 4 + 4i Find all solutions of z2 = 3 - 2i
| 1. Let z = 1+ 2i z = -2-2i, z = 3, 24 =i A. Complex arithmetic (20%) | a. Zi + Z2 b. Z1Zz sle Isles B. Determine the principle value of the argument and graph it (20%) a. 21 b. Z2 c. 23 d. 24
Simplify: 2i -1+2i
© Examples: 1. Find the direction angles of for the vector v = 2i + 3j + 4k, and show that cos?a + cos?ß + cos2y = 1. 2. Find the direction angles of the vector v= 2i + 3j – k. O P1. Find the direction angle of line determined by the origin and the point P(2,-3,6) OP2. Find the direction cosines of the line directed from P1(1, -3,4) to P2(4,3,-2).