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Popular >

simplify |e^{-i}|

Solution

simplify

e^{- i}

Solution

cos^{2} (1) + sin^{2} (1)

+1

Decimal Notation

1

Solution steps

e^{- i}

Simplify

e^{- i} : cos (1) - i sin (1)

= ∣ cos (1) - i sin (1) ∣

∣ a + bi ∣ = (a + bi) (a - bi) = a^{2} + b^{2}

With

a = cos (1), b = - sin (1)

= cos^{2} (1) + (- sin (1))^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- sin (1))^{2} = sin^{2} (1)

= cos^{2} (1) + sin^{2} (1)

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Frequently Asked Questions (FAQ)

What is |e^{-i}| ?
The solution to |e^{-i}| is sqrt(cos^2(1)+sin^2(1))