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

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вопрос

First, let's simplify the expression by combining like terms:

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

To simplify this expression, we need to find a common denominator for the two fractions. To do this, we multiply the numerator and denominator of each fraction by the conjugate of the denominator. The conjugate of (2-3i) is (2+3i) and the conjugate of (5+2i) is (5-2i).

So, we rewrite the expression as:

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

Now, we simplify each fraction separately by multiplying out the numerators and denominators:

= (4+2i+6i+i^2) / (4-9i^2) + (5-2i-5i+2i^2) / (25 - 4i^2)
= (4+2i+6i-1) / (4-9(-1)) + (5-2i-5i-2) / (25 - 4(-1))
= (3+8i) / (4+9) + (3-7i) / (25 + 4)
= (3+8i) / 13 + (3-7i) / 29

Combining the two fractions, we get:

= (29(3+8i) + 13(3-7i)) / (13*29)
= (87 + 232i + 39 - 91i) / 377
= (126 + 141i) / 377

Therefore, the simplified expression is (126 + 141i) / 377.