Question Video: Finding the Sum of Two Complex Numbers Represented on an Argand Diagram Mathematics

Using the Argand diagram shown, find the value of ๐‘งโ‚ + ๐‘งโ‚‚.

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Video Transcript

Using the Argand diagram shown, find the value of ๐‘ง sub one plus ๐‘ง sub two.

We begin by recalling that any complex number ๐‘ง can be written in the form ๐‘ฅ plus ๐‘ฆ๐‘–, where ๐‘ฅ is the real part of our complex number and ๐‘ฆ is the imaginary part. On an Argand diagram, the ๐‘ฅ-coordinate is the real part and the ๐‘ฆ-coordinate is the imaginary part. The point ๐‘ง sub one has coordinates two, three. This means that the complex number ๐‘ง sub one is equal to two plus three ๐‘–. The point ๐‘ง sub two has coordinates negative four, negative three. This means that ๐‘ง sub two is equal to the complex number negative four minus three ๐‘–.

We are asked in this question to find the value of the complex number ๐‘ง sub one plus ๐‘ง sub two. This means that we need to add two plus three ๐‘– and negative four minus three ๐‘–. Adding the real parts two and negative four gives us negative two. Adding the imaginary parts three ๐‘– and negative three ๐‘– gives us zero ๐‘– or just zero. ๐‘ง sub one plus ๐‘ง sub two is therefore equal to negative two. This corresponds to the point on the Argand diagram with coordinates negative two, zero. Even though ๐‘ง sub one and ๐‘ง sub two were complex numbers with both real and imaginary parts, ๐‘ง sub one plus ๐‘ง sub two is a real number.

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