Answer:
The right answer is figure B
Step-by-step explanation:
* Lets talk about the complex number
- The complex number z = a + bi consists of two part:
# a is the real part and represented graphically by the x-axis
# b is the imaginary part and represented graphically by the y-axis
- We can add and subtract them by adding or subtracting the real parts
together and the imaginary parts together
# Ex: if z1 = 2 + 3i and z2 = -1 - i
∴ z1 + z2 = (2 + -1) + (3 + -1)i = 1 + 2i
∴ z1 - z2 = (2 - -1) + (3 - -1)i = (2 + 1) + (3 + 1)i = 3 + 4i
* Now lets solve the problem
- Let find from the graph z1 , z2 and point A
- Look to the any graph and find z1 through the axes
- We moved 6 units on the x-axis (real part) and 7 units up
(imaginary part)
∴ z1 = 6 + 7i
- Similarly find z2 through the axes
- We moved 5 units on the x-axis (real part) and 2 units down
(imaginary part)
∴ z2 = 5 - 2i
* Now lets solve z1 - z2
∵ z1 = 6 + 7i and z2 = 5 - 2i
∴ z1 - z2 = (6 + 7i) - (5 - 2i) = (6 - 5) + (7 - -2)i = 1 + 9i
* Lets find in which figure the coordinates of A are (1 , 9)
∵ In figure A point A is (1 , 6)
∵ In figure B point A is (1 , 9)
∵ In figure C point A is (11 , 5)
∵ In figure D point A is (11 , 9)
∴ The right answer is figure B
