Question

(i-1)(3i-1)/(2-i)^2 ХЕЛП

Answer 1

(i-1)(3i-1)/((2-i)²=

(3i²-i-3i+1)/(4-4i+i²)=

(-3-4i+1)/(4-4i-1)=
(-2-4i)/(3-4i)=-(2+4i)(3+4i)/(3-4i)(3+4i)=
(-6-8i-12i-16i²)(9-16i²)=

(-20i+10)/25=10/25 -20i/25= 2/5-4i/5

Answer 2

Sure, I'd be happy to help you simplify the expression:

Let's break it down step-by-step:

Step 1: Expand the numerator (i-1)(3i-1)

(i - 1)(3i - 1) = 3i^2 - i - 3i + 1 = 3i^2 - 4i + 1

Step 2: Expand the denominator (2 - i)^2

(2 - i)^2 = (2 - i)(2 - i) = 2(2) - 2i - 2i + i^2 = 4 - 4i + i^2

Step 3: Simplify the denominator by using the fact that i^2 = -1

i^2 = -1 4 - 4i + i^2 = 4 - 4i - 1 = 3 - 4i

Now, the expression becomes:

(i - 1)(3i - 1)/(2 - i)^2 = (3i^2 - 4i + 1)/(3 - 4i)

Step 4: Combine like terms in the numerator

The expression (3i^2 - 4i + 1) simplifies to 3i^2 - 4i + 1, but remember that i^2 = -1, so:

3i^2 = 3(-1) = -3

The expression becomes:

3i^2 - 4i + 1 = -3 - 4i + 1 = -2 - 4i

Step 5: Write the simplified expression

(i - 1)(3i - 1)/(2 - i)^2 = (-2 - 4i)/(3 - 4i)

That's the simplified expression for (i - 1)(3i - 1)/(2 - i)^2.