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Express the number 1+I in polar form

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Answer to a math question Express the number 1+I in polar form

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Hank
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103 Answers
Necesitamos expresar el número

1 + i

en forma polar. Usaremos las siguientes fórmulas:

La magnitud \( r \) de un número complejo \( a + bi \) se calcula como:
r = \sqrt{a^2 + b^2}

El argumento \( \theta \) se calcula como:
\theta = \tan^{-1}\left(\frac{b}{a}\right)

En este caso, tenemos \( a = 1 \) y \( b = 1 \).

[Solução]

\sqrt{2} \left( \cos{\frac{\pi}{4}} + i \sin{\frac{\pi}{4}} \right)

[Etapa a etapa]

1. Calcular a magnitude:
r = \sqrt{1^2 + 1^2} = \sqrt{2}

2. Calcular o argumento:
\theta = \tan^{-1}\left(\frac{1}{1}\right) = \tan^{-1}(1) = \frac{\pi}{4}

3. Expressar em forma polar:
1 + i = \sqrt{2} \left( \cos{\frac{\pi}{4}} + i \sin{\frac{\pi}{4}} \right)

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