6.7 Geometric Application 6.8 Complex Numbers

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Presentation transcript:

6.7 Geometric Application 6.8 Complex Numbers

Pythagorean Theorem c2 = a2 + b2 So c = a2 + b2 a = c2 - b2 b = c2 - a2 Hypotenuse c Leg a Leg b

Examples c=? a=3 b=5 c=13 b=12 a=?

Examples A square has the diagonal of 3 2. Find the side of the square 2) Find c 3 2 c = ? 4cm

Examples using Pythagorean Theorems 2) The base of a 10 ft long guy wire is located 7 ft from the telephone pole. How high is the pole?

Draw set of complex numbers

An imaginary number is a number that can be written as: a + bi (a, b Є R, b ≠ 0) Example: -3 + 4i, or 8i

8i Example: -3 + 4i -5 Complex number a + bi (a, b Є R, a, b can be 0) Complex numbers: include real and imaginary #s Example: -3 + 4i 8i -5 We can see imaginary in engineer work

Power of i: Even power -1 or 1; Odd power –i or i

i12 = 1 i30 = -1 i17 = i i43 = -i