In the image which shows the complex number w and z+w, the value of the complex number Z is -3+6i.
How to find value of complex number from graph?
To find the value of a complex number from the graph, follow the steps below.
- On the graph where x-axis represents the real line, the distance of the point give the real number.
- On the graph where y-axis represents the imaginary line, the distance of the point give the imaginary number, which is written with complex number i.
The image shows w and z + w. The point w is 1 units left from the imaginary axis. Thus, the real number for w is -1.
This number is 2 units down. Thus, the complex number represent the point w is,
[tex]w=-1-2i[/tex] ......1
Similarly, z+w is 4 units left and 4 units up. Thus, the complex number represent z+w is,
[tex]z+w=-4+4i[/tex] ......2
Substrate equation 1 from equation 2,
[tex]z+w-w=-4+4i-(-1-2i)\\z=-4+4i+1+2i\\z=-3+6i[/tex]
Hence, In the image which shows the complex number w and z+w, the value of the complex number Z is -3+6i.
Learn more about the complex number here;
https://brainly.com/question/2218826
