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Popular >

simplificar sqrt(2)cis(pi/2)cis((3pi)/4)

Solución

simplificar

2 c i s (\frac{π}{2}) c i s (\frac{3 π}{4})

Solución

\frac{3 π ^{2} i ^{2} c ^{2} s ^{2}}{4 2}

Pasos de solución

2 c i s (\frac{π}{2}) c i s (\frac{3 π}{4})

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

ii = i^{1 + 1}

= 2 cs \frac{π}{2} c i^{1 + 1} s \frac{3 π}{4}

Sumar:

1 + 1 = 2

= 2 cs \frac{π}{2} c i^{2} s \frac{3 π}{4}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cc = c^{1 + 1}

= 2 s \frac{π}{2} c^{1 + 1} i^{2} s \frac{3 π}{4}

Sumar:

1 + 1 = 2

= 2 s \frac{π}{2} c^{2} i^{2} s \frac{3 π}{4}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

ss = s^{1 + 1}

= 2 \frac{π}{2} c^{2} i^{2} s^{1 + 1} \frac{3 π}{4}

Sumar:

1 + 1 = 2

= 2 \frac{π}{2} c^{2} i^{2} s^{2} \frac{3 π}{4}

Multiplicar fracciones:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{π 3 π 2 c ^{2} i ^{2} s ^{2}}{2 \cdot 4}

π 3 π 2 c^{2} i^{2} s^{2} = 32 π^{2} i^{2} c^{2} s^{2}

= \frac{3 2 π ^{2} i ^{2} c ^{2} s ^{2}}{2 \cdot 4}

Multiplicar los numeros:

2 \cdot 4 = 8

= \frac{3 2 π ^{2} i ^{2} c ^{2} s ^{2}}{8}

Factorizar

8 : 2^{3}

= \frac{3 2 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{3}}

Cancelar

\frac{3 π ^{2} 2 c ^{2} i ^{2} s ^{2}}{2 ^{3}} : \frac{3 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{\frac{5}{2}}}

= \frac{3 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{\frac{5}{2}}}

2^{\frac{5}{2}} = 2^{2} 2

= \frac{3 π ^{2} i ^{2} c ^{2} s ^{2}}{2 ^{2} 2}

2^{2} = 4

= \frac{3 π ^{2} i ^{2} c ^{2} s ^{2}}{4 2}

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