If 𝑟 equals five minus three 𝑖 and 𝑠 equals negative two plus four 𝑖, find three times 𝑟 plus 𝑠.
To solve three times 𝑟 plus 𝑠, we’ll substitute 𝑟 and 𝑠 with their expressions. 𝑟 is five minus three 𝑖 plus 𝑠 which is negative two plus four 𝑖. Keep the parentheses because we’re going to multiply this whole value by three.
Now, inside the parentheses, we’re going to combine like terms. We’ll add five and negative two together. That equals three. We treat the 𝑖 here like a variable, like any other variable. Negative three 𝑖 can be combined with four 𝑖. And that would be one 𝑖.
If you’re not sure what happened there, we had three negative 𝑖s and four positive 𝑖s. All of the negatives cancelled out and we were left with one remaining positive 𝑖 value.
Now, we’re going to need to multiply what’s inside the parentheses by three. We do that by distributing. Three times three equals nine and three times one 𝑖 or three times 𝑖 equals three 𝑖.
Our new expression is nine plus three 𝑖.