What is e^{(-3+20i)*0.01} ?

The solution to e^{(-3+20i)*0.01} is 0.95110…+0.19279…i

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simplify e^{(-3+20i)*0.01}

simplify

e^{(- 3 + 20 i) \cdot 0.01}

0.95110 \dots + 0.19279 \dots i

Solution steps

e^{(- 3 + 20 i) \cdot 0.01}

Apply imaginary number rule:

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

= e^{- 0.03} (cos (0.2) + i sin (0.2))

Apply exponent rule:

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

e^{- 0.03} = \frac{1}{e ^{0.03}}

= \frac{1}{e ^{0.03}} (cos (0.2) + i sin (0.2))

\frac{1}{e ^{0.03}} = 0.97044 \dots

= 0.97044 \dots (cos (0.2) + i sin (0.2))

cos (0.2) = 0.98006 \dots

= 0.97044 \dots (0.98006 \dots + i sin (0.2))

Simplify

sin (0.2) : 0.19866 \dots

= 0.97044 \dots (0.98006 \dots + 0.19866 \dots i)

Rewrite

0.97044 \dots (0.98006 \dots + 0.19866 \dots i)

in standard complex form:

0.95110 \dots + 0.19279 \dots i

= 0.95110 \dots + 0.19279 \dots i

(3, 0) y (1, - 1)

x (2 - x)

\frac{d ^{2}}{d x ^{2}} ((y) (y^{3} + 7 y - x^{3}))

- \frac{1}{s ( 3 s - 3 )}

(e^{i x} + e^{- i x})^{3}

What is e^{(-3+20i)*0.01} ?
The solution to e^{(-3+20i)*0.01} is 0.95110…+0.19279…i