Fall 1998, METBD 451 - FEA Dynamic Applications

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Homework Assignment 3

Worksheet on Complex Numbers, Complex Arithmetic

 

Rules of Complex Arithmetic:

•    or we can write: i² = -1
• Every complex number has the "Standard Form": a + bi
• a + bi = 0, only if a = b = 0
• (a + bi) + (c + di) = (a + c) + (b + d)i
• (a + bi) (c + di) = ac +bci + adi + bdi² = (ac - bd) + (bc + ad)i
• For division: multiply the numerator and the denominator by the "complex conjugate" of the denominator:
• For vectors:

1. Write in standard form:
2. Write in standard form:
3. Write in standard form.
4. Simplify:
5. Simplify:
6. Simplify:
7. Find the Real and Imaginary parts of: