Question

1. simplify each expression. write your result in the form a+bi.

a) (2 - 8i) - (9 + i)
b) (6 + i)(2 - 3i)

Explanation:

Part (a)

Step1: Distribute the subtraction

We have \((2 - 8i)-(9 + i)=2 - 8i-9 - i\)

Step2: Combine like terms (real and imaginary)

For real parts: \(2-9=-7\)
For imaginary parts: \(-8i - i=-9i\)
So the simplified form is \(-7-9i\)

Part (b)

Step1: Use the distributive property (FOIL method)

\((6 + i)(2 - 3i)=6\times2+6\times(-3i)+i\times2+i\times(-3i)\)
\(=12-18i + 2i-3i^{2}\)

Step2: Recall that \(i^{2}=-1\)

Substitute \(i^{2}=-1\) into the expression:
\(=12-16i-3\times(-1)\)
\(=12-16i + 3\)

Step3: Combine like terms (real parts)

\(12 + 3-16i=15-16i\)

Answer:

s:
a) \(\boldsymbol{-7 - 9i}\)
b) \(\boldsymbol{15-16i}\)