What is e^{(-2+i25)*0.01} ?

The solution to e^{(-2+i25)*0.01} is 0.94972…+0.24250…i

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simplify e^{(-2+i25)*0.01}

simplify

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

0.94972 \dots + 0.24250 \dots i

Solution steps

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

Apply imaginary number rule:

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

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

Apply exponent rule:

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))

Simplify

sin (0.25) : 0.24740 \dots

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

Rewrite

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

in standard complex form:

0.94972 \dots + 0.24250 \dots i

= 0.94972 \dots + 0.24250 \dots i

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lo g_{9} (x + 3) (x - 5)

(3 X + 2 Y - 16 = 0,) (5 X + 2 Y - (- 18) = 0)

(ln (t))^{2}

(2 x + 2 y y^{'} (x) = 0) \frac{1}{2}

What is e^{(-2+i25)*0.01} ?
The solution to e^{(-2+i25)*0.01} is 0.94972…+0.24250…i