What is e^{(-0.0833+0.1729i)*2} ?

The solution to e^{(-0.0833+0.1729i)*2} is 0.79642…+0.28693…i

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simplify e^{(-0.0833+0.1729i)*2}

simplify

e^{(- 0.0833 + 0.1729 i) \cdot 2}

0.79642 \dots + 0.28693 \dots i

Solution steps

e^{(- 0.0833 + 0.1729 i) \cdot 2}

Apply imaginary number rule:

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

= e^{- 0.1666} (cos (0.3458) + i sin (0.3458))

Apply exponent rule:

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

e^{- 0.1666} = \frac{1}{e ^{0.1666}}

= \frac{1}{e ^{0.1666}} (cos (0.3458) + i sin (0.3458))

\frac{1}{e ^{0.1666}} = 0.84653 \dots

= 0.84653 \dots (cos (0.3458) + i sin (0.3458))

cos (0.3458) = 0.94080 \dots

= 0.84653 \dots (0.94080 \dots + i sin (0.3458))

Simplify

sin (0.3458) : 0.33894 \dots

= 0.84653 \dots (0.94080 \dots + 0.33894 \dots i)

Rewrite

0.84653 \dots (0.94080 \dots + 0.33894 \dots i)

in standard complex form:

0.79642 \dots + 0.28693 \dots i

= 0.79642 \dots + 0.28693 \dots i

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p (- 5, 4, 2) e Q (3, - 3, 9)

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What is e^{(-0.0833+0.1729i)*2} ?
The solution to e^{(-0.0833+0.1729i)*2} is 0.79642…+0.28693…i