Video: US-SAT04S3-Q14-152170652363

Given that 𝑖 = βˆšβˆ’1, find (2 βˆ’ 7𝑖) βˆ’ (3 βˆ’ 2𝑖).

01:30

Video Transcript

Given that 𝑖 is equal to the square root of negative one, find two minus seven 𝑖 minus three minus two 𝑖.

In order to answer this question, we need to group or collect the real terms and then, separately, the imaginary terms. The real terms inside the brackets are two and three. And the imaginary terms are negative seven 𝑖 and negative two 𝑖. Let’s firstly consider the real terms. We have a two in the first bracket and a three in the second bracket. And We want to subtract these. Two minus three is equal to negative one. The real term in our answer will be negative one.

Now, let’s consider the imaginary terms negative seven 𝑖 and negative two 𝑖. We want to subtract negative two 𝑖 from negative seven 𝑖. Subtracting a negative number is the same as adding that number. Therefore, we have negative seven 𝑖 plus two 𝑖. Negative seven plus two is equal to negative five. Therefore, our imaginary term is negative five 𝑖. Two minus seven 𝑖 minus three minus two 𝑖 is equal to negative one minus five 𝑖.

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