化简 e^{(-2+i25)*0.01}

解答

化简

e^{(- 2 + i 25) \cdot 0.01}

0.94972 \dots + 0.24250 \dots i

求解步骤

e^{(- 2 + i 25) \cdot 0.01}

使用虚数运算法则:

e^{a + ib} = e^{a} (cos (b) + i sin (b))

= e^{- 0.02} (cos (0.25) + i sin (0.25))

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

e^{- 0.02} = \frac{1}{e ^{0.02}}

= \frac{1}{e ^{0.02}} (cos (0.25) + i sin (0.25))

\frac{1}{e ^{0.02}} = 0.98019 \dots

= 0.98019 \dots (cos (0.25) + i sin (0.25))

cos (0.25) = 0.96891 \dots

= 0.98019 \dots (0.96891 \dots + i sin (0.25))

化简

sin (0.25) : 0.24740 \dots

= 0.98019 \dots (0.96891 \dots + 0.24740 \dots i)

将

0.98019 \dots (0.96891 \dots + 0.24740 \dots i)

改写成标准复数形式:

0.94972 \dots + 0.24250 \dots i

= 0.94972 \dots + 0.24250 \dots i

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