What is maclaurin e^{iθ} ?

The answer to maclaurin e^{iθ} is 1+iθ-1/2 θ^2-i/6 θ^3+1/24 θ^4+\ldots

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maclaurin e^{iθ}

maclaurin

e^{i θ}

1 + i θ - \frac{1}{2} θ^{2} - \frac{i}{6} θ^{3} + \frac{1}{24} θ^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d θ} ( e ^{i θ} ) ( 0 )}{1 !} θ + \frac{\frac{d ^{2}}{d θ ^{2}} ( e ^{i θ} ) ( 0 )}{2 !} θ^{2} + \frac{\frac{d ^{3}}{d θ ^{3}} ( e ^{i θ} ) ( 0 )}{3 !} θ^{3} + \dots

Evaluate Derivatives

= 1 + \frac{i}{1 !} θ + \frac{- 1}{2 !} θ^{2} + \frac{- i}{3 !} θ^{3} + \frac{1}{4 !} θ^{4} + \dots

Refine

= 1 + i θ - \frac{1}{2} θ^{2} - \frac{i}{6} θ^{3} + \frac{1}{24} θ^{4} + \dots

\frac{d}{d z} (e^{i z})

\frac{d y}{d t} = 1.7 y

f (x) = (x - 5) (x + 1)

\int 4 e^{3 x + e^{3 x}} d x

\frac{d y}{d x}, 8 x + 3 y = 7

What is maclaurin e^{iθ} ?
The answer to maclaurin e^{iθ} is 1+iθ-1/2 θ^2-i/6 θ^3+1/24 θ^4+\ldots