Find all the values of (1 + 2i)1/3
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.)
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. -
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).
Using Euler's formula, state all possible values of the expressions: A. e^(i3pi) B. (1)^(1/4) C. e^(1+i2) D. arg(2-2i) E. Arg(2-2i)
For a = 2i - 3j + 4k, b = 5i + 2j + 6k, find a times b For a = -5i + 3j - 6k, b = 2i - 2j + 3k, find a times b For a = 7i - j + 3k, b = i + 3j - 4k, find a times b For a = 2i + 3j + 5k, b = 4i + 2j - 3k, find a times b
Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i)
Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i)
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find m distinct m-th roots (z/m) for the following values of m. You may leave your answer in exponential form. (i) m = 2 (ii) m=4 (iii) m = 10 (iv) m= 45 (v) m = 100