PRECALCULUS

HW 13: p. 583/ 12 – 34 even, 39 12) -3.7 + 7.4i N 14) –i 16) 0 18) 9 – 7i 20) -7 + 4i 22) -15 + 8i 24) -8 + 3√3i 26) -10/17 + (11/17)I 28) x² + 1 = 0 30) 12 – 31i 32) (1/6 - √6/3) + (√3/3 + √2/6)i 34) 13/25 – (9/25)i PC08 Monday, 3/03/08

Beginning of HW 14:

“Talent without discipline is like an octopus on roller skates. Monday, 3/03/08 “Talent without discipline is like an octopus on roller skates. There’s plenty of movement, but you never know if it’s going to be forward, backward, or sideways.” H. Jackson Brown, Jr. pc08

9-6 The Complex Plane and Polar Form of Complex Numbers Solving complex equations ex. Solve 3x + 2y – 7i = 12 + xi – 3yi for the real numbers x and y. x = 2 and y = 3

Complex Plane (Argand Plane) (*NOT a new version of the xy plane!*) Absolute Value of a Complex Number (*not the same meaning as before*) If z = a + bi, then |z| = √(a² + b²) ex. Graph each number in the complex plane and find its absolute value. a) z = 4 + 3i b) z = 2.5i

Polar Form of a Complex Number (“Trig. Form”) sq17cis4.96, sq13cis3.73 ex. Convert rectangular form to polar form: a) 1 – 4i b) -3 – 2i HINT: Same process as before r = |z| = √(a² + b²) tan ϑ = y/x NOTE: usually in radians Abbr. z = √17cis4.96

NOTE: r is called the modulus and ϑ is called the argument or amplitude. Converting polar to rectangular: (x, y) = (rcos ϑ, rsin ϑ) ex. Graph 2(cos 5π/6 + i sin5π/6) then express it in rectangular form. HW 14: p. 590/ 16 – 44 even

notes