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Question
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
Solution
Given that: `(1 + i)^2/(2 - i)` = x + iy
⇒ `(1 + i^2 + 2i)/(2 - i)` = x + iy
⇒ `(1 - 1 + 2i)/(2 - i)` = x + iy
⇒ `(2i)/(2 - i)` = x + iy
⇒ `(2i(2 + i))/((2 - i)(2 + i))` = x + iy
⇒ `(4i + 2i^2)/(4 - i^2)` = x + iy
⇒ `(4i - 2)/(4 + 1)` = x + iy ......[∵ i2 = –1]
⇒ `(-2 + 4i)/5` = x + iy
⇒ `(-2)/5 + 4/5 i` = x + iy
Comparing the real and imaginary parts,
We get x = `(-2)/5` and y = `4/5`
Hence, x + y = `(-2)/5 + 4/5 = 2/5`.
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