Question Video: Identifying Complex Numbers on Argand Diagrams Mathematics • Third Year of Secondary School

Video Transcript

Using the Argand diagram shown, find the value of two 𝑧 one plus 𝑧 two.

We know that any complex number 𝑧 can be written in the form 𝑎 plus 𝑏𝑖, where 𝑎 is the real component and 𝑏 the imaginary component. On an Argand diagram, the horizontal axis corresponds to the real component and the vertical axis the imaginary component. This means that 𝑧 sub one corresponds to the complex number two minus three 𝑖. As the point 𝑧 sub two has coordinates six, two, it corresponds to the complex number six plus two 𝑖.

We need to calculate two 𝑧 one plus 𝑧 two. This is equal to two multiplied by two minus three 𝑖 plus six plus two 𝑖. Distributing the parentheses or expanding the brackets gives us four minus six 𝑖. We can then group or collect the like terms. The real parts sum to give us 10. Negative six 𝑖 plus two 𝑖 is equal to negative four 𝑖. The complex number two 𝑧 one plus 𝑧 two is equal to 10 minus four 𝑖.