Question

(-5,7+3,3)^(-3,5)-8,9-0,4

Answer 1

-9.2995427526 очень трудно

Answer 2

To evaluate the expression (-5,7+3,3)^(-3,5) - 8,9 - 0,4, we can simplify it step by step:

1. (-5,7+3,3)^(-3,5): We need to evaluate the expression inside the parentheses first. -5,7 + 3,3 = -2,4 (adding the real parts and imaginary parts separately) So, (-5,7+3,3)^(-3,5) becomes (-2,4)^(-3,5).

2. Now, let's calculate (-2,4)^(-3,5) using polar form: First, convert (-2,4) to polar form. The magnitude (r) can be calculated using the absolute value of the complex number: r = |(-2,4)| = √((-2)^2 + 4^2) = √(4 + 16) = √20 = 2√5

   The argument (θ) can be calculated using the inverse tangent (arctan) of the imaginary part divided by the real part: θ = arctan(4/(-2)) = arctan(-2) = -63.43° (rounded to two decimal places)

   Now, we have (-2,4) in polar form as (2√5, -63.43°).

   To raise it to the power of (-3,5), we need to multiply the magnitude by the exponent and add the argument with the product: (2√5, -63.43°)^(-3,5) = (2√5)^(-3,5) * e^(-3,5 * -63.43°)

   Using the polar exponentiation formula: (r, θ)^n = (r^n, nθ) (2√5, -63.43°)^(-3,5) = (2√5)^(-3,5) * e^(-3,5 * -63.43°)

   Calculating (2√5)^(-3,5): (2√5)^(-3,5) = 1/(2√5)^(3,5) = 1/(2^3.5 * 5^1.75)

   Calculating e^(-3,5 * -63.43°): e^(-3,5 * -63.43°) = e^(3,5 * 63.43°)

   Note: "e" represents the mathematical constant approximately equal to 2.71828.

3. Subtracting 8,9 - 0,4: 8,9 - 0,4 = 8,5 (subtracting the real parts and imaginary parts separately)

Finally, the expression (-5,7+3,3)^(-3,5) - 8,9 - 0,4 simplifies to:

(2√5)^(-3,5) * e^(3,5 * 63.43°) - 8,5