Download Homework 1 in MA205

Homework 1 in MA205
Complex Numbers (sections 1.1 and 1.2)
Let z = -2 + 3i and w = 1 + i.
1.
(a). Graph z and z.
(b). Compute z and arg(z).
2.
(a). Compute the complex number zw.
(b). Compute the complex number z/w.
3.
(a). Solve for the complex number such that
2  4i
 7  i.
z i
(a). Find both the complex numbers such that
z 2  7  i.
Vectors in the Plane (sections 1.3 and 1.4)
Let
4.
a  [2  1] and b  [3 2].
(a). Graph the vectors a and b .
(b). Compute a , 7a, a  b, a  b and 2a  3b.
5.
(a). Solve for x when 2 x  [6  10].
(b). Solve for x when 2 x  a  5b.
6.
(a). Compute the dot product of a and b : a  b
(b). Find the angle between the vectors a and b .