MATH215 Lecture 9: note9

• School: University of Alberta
• Department: Mathematics
• Course: MATH215
• Professor: Alexander Litvak

Document Summary

Complex numbers: complex numbers a complex number can be represented by an expression of the form a + bi, where a and b are real numbers and i is a symbol with the property that i2 = 1. Let a + bi and c + di be two complex numbers. The conjugate of a + bi is a bi. Note that (a + bi)(a bi) = a2 + b2 0. Xk=0 ( 1)k (2k + 1)! x2k+1 = cos x + i sin x: the integral of a complex-valued function suppose a and b are real numbers. By euler"s formula we have e(a+bi)x = eaxeibx = eax(cid:0)cos(bx) + i sin(bx)(cid:1). Z e(a+bi)x dx = e(a+bi)x a + bi. + c = eax(cid:0)cos(bx) + i sin(bx)(cid:1) a + bi. Z eax cos(bx) dx = eax a2 + b2(cid:0)a cos(bx) + b sin(bx)(cid:1) + c.