Question

1+i/1-2i - (4/5 - 2/5 i)

Answer 1

В приложении ответ /$#@!/$##@

Answer 2

To simplify the expression (1 + i) / (1 - 2i) - (4/5 - 2/5i), you can follow these steps:

1. Find a common denominator for the two fractions in the expression.
2. Combine the fractions.
3. Simplify the result.

Let's go through it step by step:

1. Find a common denominator for (1 - 2i) and (5) in the second term:

(1 + i) / (1 - 2i) - (4/5 - 2/5i) = (1 + i) / (1 - 2i) - (4(1 - 2i) / 5(1 - 2i))

2. Combine the fractions:

[(1 + i) - (4(1 - 2i)) / 5(1 - 2i)]

3. Simplify the numerator:

(1 + i - 4 + 8i) / 5(1 - 2i)

Combine like terms in the numerator:

(-3 + 9i) / 5(1 - 2i)

Now, you have the simplified expression:

(-3 + 9i) / (5 - 10i)

If you'd like to further simplify it, you can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (5 + 10i) to eliminate the imaginary part in the denominator:

[(-3 + 9i) * (5 + 10i)] / [(5 - 10i) * (5 + 10i)]

Simplify the numerator and denominator:

[(-15 - 30i + 45i - 90)] / (25 + 100)

Combine like terms:

(-105 - 30i) / 125

Now, you have the final simplified expression:

(-21 - 6i) / 25