rev6 - z 1 | + | z 2 | , and d. | z 1-z 2 | | z 1 | - | z 2...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics (PHZ) 3113 Florida Atlantic University Mathematical Physics Fall, 2009 Review Problems VI Recommended Reading: Chow, pp. 233–238. 1. (Chow 6.2) Given the complex numbers z 1 := 3 + 4i 3 - 4i and z 2 := ± 1 + 2i 1 - 3i ² 2 , find their polar forms, complex conjugates, moduli, product, and quotients. 2. (Chow 6.3) The absolute value or modulus of a complex number z =: x + i y is defined as | z | = zz * = p x 2 + y 2 . If z 1 and z 2 are complex numbers, show that: a. | z 1 z 2 | = | z 1 || z 2 | , b. | z 1 /z 2 | = | z 1 | / | z 2 | for z 2 6 = 0, c. | z 1 + z 2 | ≤ |
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: z 1 | + | z 2 | , and d. | z 1-z 2 | | z 1 | - | z 2 | . 3. (Chow 6.4) Find all possible complex values of z (a) := 5 -32 and z (b) := 3 1 + i , and plot them in the complex plane. 4. (Chow 6.5) Use De Moivres theorem to show that a. cos 5 = 16 cos 5 -20 cos 3 + 5 cos , and b. sin 5 = 5 cos 4 sin -10 cos 2 sin 3 + sin 5 ....
View Full Document

Ask a homework question - tutors are online