Question

a). (9e^20i)×(4e^35i)

b). (9e^20i) ÷ (4e^35i)

c). (4e^35i)²

d). √9e^20i​

Answer 1

Explicación paso a paso:

En general, se aplica la propiedad de los números complejos $e^{a i}= (-1)^{\frac{a}{\pi}}$

a)

$(9e^{20i})(4e^{35i})=9e^{20i}\cdot 4e^{35i}$

$9e^{20i}\cdot 4e^{35i}$

$9(-1)^{\frac{20}{\pi}}\cdot 4(-1)^{\frac{35}{\pi}}$

$36(-1)^{\frac{55}{\pi}}$

b)

$(9e^{20i}) \div (4e^{35i})=\frac{9e^{20i} }{4e^{35i} }$

$\frac{9e^{20i} }{4e^{35i} }$

$\frac{9(-1)^{\frac{20}{\pi}} }{4(-1)^{\frac{35}{\pi}} }$

$\frac{9}{4(-1)^{\frac{15}{\pi}} }$

c)

$(4e^{35i})^{2} = (4(-1)^{\frac{35}{\pi}})^{2}$

$(4(-1)^{\frac{35}{\pi}})^{2}$

$16(-1)^{\frac{70}{\pi}}$

d)

$\sqrt{9e^{20i}} = \sqrt{9(-1)^{\frac{20}{\pi}}}$

$\sqrt{9(-1)^{\frac{20}{\pi}}}$

$3 \sqrt{(-1)^{\frac{20}{\pi}}}$