Chap 1 The Number System

# Solve the equation z 2 z 1 0 if the solutions are z1

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

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

Unformatted text preview: ent in part (b)? f) Let a, b ∈ R be ﬁxed positive real numbers. Repeat steps (a)–(e) with a + bi in place of 3 + 4i. g) What can we say about the eﬀect of multiplying a complex number by i? h) What can we say about the eﬀect of multiplying a complex number by 2i? 9. Let z1 = 2 + 4i and z2 = 1 (1 − 5i). Find each of the following numbers: 2 a) z1 z2 b) (z1 + 2z2 )2 c) iz1 + 2z2 √ 10. Let z1 = 5, z2 = 3 + 4i and z3 = 1 − 3i. Evaluate each of the following numbers: a) z1 b) z2 c) z1 − z2 d) z2 z3 e) Re(z1 /z2 ) f) arg z3 11. Suppose that z = x + iy , where x, y ∈ R and i2 = −1. Write down each of the following numbers in terms of x, y and i: zz a) Re(z ) b) Im(z ) c) z d) |z |2 e) Im(z −1 ) f) |z |2 12. Express each of the following numbers in the form x + y i, where x, y ∈ R: a) (1 + 3i)3 b) (3 − 2i)2 − (3 + 2i)2 3 + 4i c) (1 + i + i2 + i3 )100 d) 5 + 6i 13. Find the real and imaginary parts of each of the following numbers: 1+i 1 + 2i x + yi a) , b) c) . 1−i 3 + 4i i 14. Suppose that a + bi = c + di,...
View Full Document

## This note was uploaded on 02/01/2009 for the course MATH 2343124 taught by Professor Staff during the Fall '08 term at UCSD.

Ask a homework question - tutors are online