1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

1 8 CHAPTER 1 • COMPLEX NUMBERS

y

(0, y)

P = (x, y) = z

llm(z}I

!Re(z)I
+----~--1--x
0 = (0, 0) Q = (x, 0)
Figure 1- 7 The moduli of z and its
components.

Figure 1.9 The triangle inequality.

y

(0, y)

• 
  
  
  
  • -- - - -~z = (x, y)
    / : =x+iy
  
  
  
  

Figure 1.8 The geometry of negation

and conjugation.

An important application of Identity (1-22) is its use in establishing the triangle

inequality, which states that the sum of the lengths of two sides of a. triangle is

greater than or equal to the length of the third side. Figure 1.9 illustrates this

inequality.