Question

Express the quantities below in a+bi form, and graph the corresponding points on the complex plane. If you use one set of axes, be sure to label each point appropriat (1+i)-(1-i), (1+i)(1-i), i(2-i)(1+2i).

Answer 1

Explanation:

As we know that

Complex number written as

Z = x + i y

x is the real part (on real axis).

y is the imaginary part(on imaginary axis).

For (1+i)-(1-i):

Z= (1+i)-(1-i)

Z = 1 + i - 1 + i

Z=2 i

So x= 0 ,y= 2

For (1+i)(1-i):

Z= (1+i)(1-i) = 1 - i² ( i² = 1)

Z = 1 - (-1) = 2

So x= 2 and y= 0

For i(2-i)(1+2i):

Z= i(2-i)(1+2i) = (2 i- i²) (1+2i)

Z= (2i + 1) (1+2i)

Z = 2i +1 +4i² + 2i

Z= 4i + 1 - 4

Z= - 3+ 4 i

x = - 3 and y =4