Answer:
2nd, 3rd and 5th options are correct.
Step by step explanation:
We are asked to find which of the given operations involving complex numbers have solutions represented by point A on the graph.
We can see that point A lies on (1,-2i). Let us see which of our given expressions give us coordinates of point A.
1. [tex](4+i)+3(1+i)[/tex]
[tex]4+i+3+3i[/tex]
[tex]4+3+i+3i[/tex]
[tex]7+4i[/tex]
We can see that our 1st option is incorrect.
2. [tex](4+i)-3(1+i)[/tex]
[tex]4+i-3-3i[/tex]
[tex]4-3-3i+i[/tex]
[tex]1-2i[/tex]
We can see that our 2nd option is correct.
3. [tex](4+i)+(-3-3i)[/tex]
[tex]4+i-3-3i[/tex]
[tex]4-3+i-3i[/tex]
[tex]1-2i[/tex]
We can see that our 3rd option is correct.
4. [tex](4+i)+(3-3i)[/tex]
[tex]4+i+3-3i[/tex]
[tex]4+3+i-3i[/tex]
[tex]7-2i[/tex]
Upon simplifying our expression we got [tex]7-2i[/tex] which is not equal to coordinates of point A. Therefore, 4th option is incorrect.
5. [tex](4+i)-(3+3i)[/tex]
[tex]4+i-3-3i[/tex]
[tex]4-3+i-3i[/tex]
[tex]1-2i[/tex]
Upon simplifying our expression we got coordinates of point A. Therefore, 5th option is correct indeed.
The correct option is the third option
Given,
From the graph we have,
[tex]z_1=4+i\\z_2=1+i\\z_3=-3-3i[/tex]
For A we have,
[tex]z_A=1-2i\\z_1+z_3=(4+i)+(-3-3i)[/tex]
Hence, the third option is correct.
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