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Using the Argand diagram shown, find the value of ๐งโ + ๐งโ.

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

We begin by recalling that any complex number ๐ง can be written in the form ๐ฅ plus ๐ฆ๐, where ๐ฅ is the real part of our complex number and ๐ฆ is the imaginary part. On an Argand diagram, the ๐ฅ-coordinate is the real part and the ๐ฆ-coordinate is the imaginary part. The point ๐ง sub one has coordinates two, three. This means that the complex number ๐ง sub one is equal to two plus three ๐. The point ๐ง sub two has coordinates negative four, negative three. This means that ๐ง 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 ๐ง sub one plus ๐ง 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. ๐ง sub one plus ๐ง sub two is therefore equal to negative two. This corresponds to the point on the Argand diagram with coordinates negative two, zero. Even though ๐ง sub one and ๐ง sub two were complex numbers with both real and imaginary parts, ๐ง sub one plus ๐ง sub two is a real number.

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