Explanation:
To simplify the expression (−12+10i)−(−8+i) into the form a + bi, we can follow these steps:
Step 1: Distribute the negative sign to the terms inside the parentheses:
(−12+10i)−(−8+i) = −12+10i+8−i
Step 2: Combine like terms:
−12+10i+8−i = (−12+8)+(10i−i) = −4+9i
Therefore, the expression (−12+10i)−(−8+i) simplifies to −4+9i in the form a + bi.
Now, let's practice with a similar problem:
Simplify the expression (5−3i)−(−2+4i) into the form a + bi.
Step 1: Distribute the negative sign to the terms inside the parentheses:
(5−3i)−(−2+4i) = 5−3i+2−4i
Step 2: Combine like terms:
5−3i+2−4i = (5+2)+(-3i-4i) = 7-7i
Therefore, the expression (5−3i)−(−2+4i) simplifies to 7-7i in the form a + bi.
Now, it's your turn to practice. Simplify the expression (−6+2i)−(−3−5i) into the form a + bi.