𝑧 equals five plus two 𝑖, what is Re 𝑧?
The first thing to do when we’re trying to solve this problem is actually to understand which different parts it means. Well, 𝑧 what this is is that’s a complex number. So we can say that our complex number is equal to five plus two 𝑖. And the other part we look at is Re 𝑧 and what this means is the real part. So this means what is the real part of our complex number.
Well, if we actually have our complex number in this form, so 𝑧 is equal to 𝑎 plus 𝑏𝑖, then the parts 𝑎 and 𝑏 actually represent different parts of our complex number. So our 𝑏 which is the coefficient of 𝑖 is actually Im 𝑧. What this means is that it’s actually the imaginary part of our complex number. Okay, great, then 𝑎, so the 𝑎 part of our complex number. What this is is actually the Re 𝑧 which we already spoke about earlier and is in fact the real part of our complex number.
Okay, great, so now we know which each part of our complex number is. We can go back and solve our problem — actually find the real part of our complex number. So if we take a look back at our complex number. We’ve got 𝑧 is equal to five plus two 𝑖. So therefore, our 𝑎 part is equal to five and our 𝑏 part is equal to two.
So therefore, we can say that if we have the complex number 𝑧 is equal to five plus two 𝑖, then we know that the real part of our complex number is going to be equal to five.