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Unformatted text preview: a2 + b2
b
θ = arctan
a a + bi = M (cos θ + i sin θ)
is sometimes called the
argument or phase of a + bi. θ Complex number review Complex number review
• Toward Euler’s formula Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2! Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2!
x2
x4
+
− ···
• What function has Taylor series 1 −
2!
4!
(A) cos x (C) ex (B) sin x (D) ln x Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2!
x2
x4
+
− ···
• What function has Taylor series 1 −
2!
4!
(A) cos x (C) ex (B) sin x (D) ln x Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2!
x3
x5
+
− ···
• What function has Taylor series x −
3!
5!
(A) cos x (C) ex (B) sin x (D) ln x Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2!
x3
x5
+
− ···
• What function has Taylor series x −
3!
5!
(A) cos x (C) ex (B) sin x (D) ln x Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be represented as f (x0 )
2
f (x) = f (x0 ) + f (x0 )(x − x0 ) +
(x − x0 ) + · · ·
2!
x2
x3
+
+ ···
• What function has Taylor series 1 + x +
2!
3!
(A) cos x (C) ex (B) sin x (D) ln x Complex number review
• Toward Euler’s formula
• Taylor series  recall that a function can be rep...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.
 Spring '13
 EricCytrynbaum
 Differential Equations, Equations, Complex Numbers

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