What is e^{(-3+2.646i)*0.1} ?

The solution to e^{(-3+2.646i)*0.1} is 0.71503…+0.19374…i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{(-3+2.646i)*0.1}

simplify

e^{(- 3 + 2.646 i) \cdot 0.1}

0.71503 \dots + 0.19374 \dots i

Solution steps

e^{(- 3 + 2.646 i) \cdot 0.1}

Apply imaginary number rule:

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

= e^{- 0.3} (cos (0.2646) + i sin (0.2646))

Apply exponent rule:

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

e^{- 0.3} = \frac{1}{e ^{0.3}}

= \frac{1}{e ^{0.3}} (cos (0.2646) + i sin (0.2646))

\frac{1}{e ^{0.3}} = 0.74081 \dots

= 0.74081 \dots (cos (0.2646) + i sin (0.2646))

cos (0.2646) = 0.96519 \dots

= 0.74081 \dots (0.96519 \dots + i sin (0.2646))

Simplify

sin (0.2646) : 0.26152 \dots

= 0.74081 \dots (0.96519 \dots + 0.26152 \dots i)

Rewrite

0.74081 \dots (0.96519 \dots + 0.26152 \dots i)

in standard complex form:

0.71503 \dots + 0.19374 \dots i

= 0.71503 \dots + 0.19374 \dots i

A (- 9, - 4) C (- 1, - 6) E (- 4, - 3)

\frac{1}{x \cdot ( x ^{3} - 2 x - 4 )}

J (- 5, - 2) k (5, - 4)

A (6, 2) B (2, - 3) C (- 2, 2)

2^{x - 2} (1 - x ln (2))

What is e^{(-3+2.646i)*0.1} ?
The solution to e^{(-3+2.646i)*0.1} is 0.71503…+0.19374…i