Video: Finding the Real Part of the Sum or Difference of Two Complex Numbers

If π‘Ÿ = 5 + 2𝑖 and 𝑠 = 9 βˆ’ 𝑖, find Re (π‘Ÿ βˆ’ 𝑠).

01:36

Video Transcript

If π‘Ÿ equals five plus two 𝑖 and 𝑠 equals nine minus 𝑖, find the real part of π‘Ÿ minus 𝑠.

Here we have two complex numbers to find as five plus two 𝑖 and nine minus 𝑖. We can see that the real part of π‘Ÿ is five and the real part of 𝑠 is nine. The imaginary part of π‘Ÿ is two and the imaginary part of 𝑠 is negative one. We’re being asked to find the real part of the difference between π‘Ÿ and 𝑠. And we could absolutely work out the entire answer to π‘Ÿ minus 𝑠 by collecting like terms. That’s five plus two 𝑖 minus nine minus 𝑖.

It’s important that we use these parentheses here because it reminds us that we’re subtracting everything inside these brackets, nine minus 𝑖. If we distribute these parentheses, we get five plus two 𝑖 minus nine plus 𝑖, since subtracting a negative is the same as adding a positive. Then we would simplify by collecting like terms. However, that’s probably a little more work than we really need to do.

In fact, we recall that, to subtract complex numbers, we simply subtract the real parts and then subtract the imaginary parts separately. We’re being asked to work out the real parts of the complex number π‘Ÿ minus 𝑠. So actually, we just need to subtract the real part of 𝑠 from the real part of π‘Ÿ. We can formalise this and say that the real part of π‘Ÿ minus 𝑠 equals the real part of π‘Ÿ minus the real part of 𝑠. We already saw that the real part of π‘Ÿ is five and the real part of 𝑠 is nine. Five minus nine is negative four. So the real part of π‘Ÿ minus 𝑠 in this case is negative four.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.