3_5_ex_sol

# 3_5_ex_sol - Section 3.5 Example Solutions Instructor Ms...

This preview shows pages 1–2. Sign up to view the full content.

Instructor: Ms. Hoa Nguyen ([email protected]) 1 Reminder of the Complex Numbers Conjugate: If z = a + bi , then the conjugate of z is ¯ z = a - bi . i 2 = - 1 because - 1 = i . z ¯ z = a 2 + b 2 = | z | 2 . Why? Because z ¯ z = ( a + bi )( a - bi ) = a 2 - abi + abi - b 2 i 2 = a 2 + b 2 . So the multiplication of a complex number z with its conjugate ¯ z is equal to the sum of the real part a squared and the imaginary part b squared. Division: If z = a + bi and w = c + di , then z w = z · ¯ w w ¯ w = z · ¯ w c 2 + d 2 because w ¯ w = c 2 + d 2 . Example 1 This is the division of complex numbers z w where z = 2 + i and w = 1 - 3 i . As suggested in the reminder, multiply the conjugate ¯ w = 1 + 3 i to the numerator and denominator of the fraction, i.e., z w = z · ¯ w w ¯ w = (2+ i )(1+3 i ) 1 2 +( - 3) 2 = - 1+7 i 10 because z · ¯ w = (2+ i )(1+3 i ) = 2+6 i + i +3 i 2 = - 1 + 7 i and w ¯ w = (1 - 3 i )(1 + 3 i ) = 1 + 3 i - 3 i

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/23/2011 for the course MAC 1147 taught by Professor Nuegyen during the Spring '11 term at FSU.

### Page1 / 3

3_5_ex_sol - Section 3.5 Example Solutions Instructor Ms...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online