Step by step
The question
Question: work out (10 − 5i)/5.
10 − 5i5
Remember: i is the square root of minus 1.
So i squared is minus 1.
i = √(−1)
i² = −1
1 Split the fraction
The bottom is a plain number: 5.
So each part on top is divided by it.
a + bc = ac + bc
10/5, and 5i/5.
= 105 − 5i5
10/5 is 2.
5/5 is 1.
So the answer is 2 − i.
= 2 − i
2 Check
Let's check: times 5 undoes divided by 5.
We get 10 − 5i again.
It works!
Check: (2 − i) × 5 = 10 − 5i
Let's look back.
First: split the fraction.
Last: check.
Answer
= 2 − i