Write the expression (-2 + 8i) - (2 - 7i) in the standard form a + bi.

Step-by-step solution

1. 1

   Distribute the subtraction over the whole second number. Subtracting a complex number means subtracting both of its parts: $(-2+8i)-(2-7i)=-2+8i-2+7i$. The sign of the imaginary part flips from $-7i$ to $+7i$; missing this is the usual mistake.

2. 2

   Group real terms with real terms. The real parts are $-2$ and $-2$, giving $-2-2=-4$. Real and imaginary parts never mix, because $i$ is not a real multiple of $1$.

3. 3

   Group the imaginary terms. The imaginary parts are $8i$ and $+7i$, giving $8i+7i=15i$. Only the coefficients add.

4. 4

   Assemble the standard form. Writing the real part first and the imaginary part second gives $-4+15i$, so $a=-4$ and $b=15$.

5. 5

   Sanity-check with the reverse operation. Adding the subtrahend back: $(-4+15i)+(2-7i)=-2+8i$, which is the original first number, so the subtraction was carried out correctly.