What number must we add to $3-5i$ to get $2+7i$? Here $i$ denotes the imaginary unit $\sqrt{-1}$.

Let the unknown (complex) number be a + bi

Then 3 - 5i + a + bi = 2 + 7i

Subtract 3 - 5i from both sides: a + bi = 2 + 7i - 3 + 5i or a + bi = -1 + 12i

Equating real and imaginery parts we have: a = -1, b = 12.

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So what number do you have to add?

The number you add is the complex number a + bi, which here is -1 + 12i.

Oops sorry I got it