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3_Complex

# 3_Complex - 3 π 2 in Cartesian form ex Evaluate z = 1-i 3...

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Complex Numbers Complex numbers have the form z = x + iy (z = x + yi) x is the real part and y is the imaginary part. ex. 3 + 3i 5 - i 3 i = -1 i 2 = ( -1) 2 = -1 The conjugate of z = a + b i is z = a - b i . The conjugate of z = a - b i is z = a + b i . Operations/Definitions 1. a + bi = c + di a = c and b = d 2. a + bi ( 29 + c + di ( 29 = a + c ( 29 + b + d ( 29 i 3. a + bi ( 29 c + di ( 29 = ac + adi + bci + bdi 2 = ( ac - bd ) + ( ad + bc ) i 4. a + bi ( 29 c + di ( 29 = a + bi ( 29 c - di ( 29 c + di ( 29 c - di ( 29 = ac - adi + bci - bdi 2 ( 29 c 2 - d 2 i 2 = ac + bd ( 29 + bc - ad ( 29 i c 2 + d 2

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ex. x + iy = 3 + 4 i ex. (2 - 3 i ) + (5 + i ) ex. (2 - 3 i )( 5 + i ) ex. 5 + i 2 - 3 i ex.
1 - 4 + 3 i Graphing The modulus or absolute value, z , of a complex number is its distance to the origin. z = x 2 + y 2 If z = 2 - 3 i , th en z = 2 2 + - 1 ( 29 2 = 5 . z = r . Since

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z = x + iy z = r cos θ+ ir sin θ z = r cos i sin ( 29 Euler’s formula: e i = co s + i s in So z = re i (polar form of a complex number) z = x + iy (Cartesian form of a complex number) ex. Write z =- 1 + i in polar form z = re i .
ex. Write z = 5 e i

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Unformatted text preview: 3 π 2 in Cartesian form. ex. Evaluate z = 1-i 3 ( 29 10 . Write it in both Cartesian and polar forms. Roots ex. Find the fifth roots of 32. 1. Write the number in polar form. 2. Find one fifth root. 3. The other roots are spaced evenly around a circle at intervals of 2 π # of roo ts = 2 5 ex. Find the fourth roots of z =-81 2-813 2 i . Do: 1. Let z = 3 + i , w = 2 i Find z 1 w 2. Write (1.) in polar form. 3. Write 3 e i π 6 in Cartesian form. 4. Find the cube roots of –64i. Remember that r 0. ≥...
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3_Complex - 3 π 2 in Cartesian form ex Evaluate z = 1-i 3...

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