Question

Perform the indicated arithmetic operations for complex numbers z = −4 + 5i and w = −1 − 2i.

a. z + w
b. z − w
c. z + 2w
d. z − z
e. Explain how you ad and subtract complex numbers.

Answer 1

(a) 3i-5

(b) 3+7i

(c) -6+i

(d) 0

Explanation:

We have given two complex numbers z = -4 + 5 i and w = -1 - 2 i

We have to perform following operation

(a)
`z+w=-4+5i-1-2i=3i-5`

(b)
`z-w=-4+5i-(-1-2i)=-4+5i+1+2i=-3+7i`

(c)
`z+w=-4+5i+2* (-1-2i)=-4+5i-2-4i=-6+i`

(d)
`z-z=-4+5i-(-4+5i)=0`

(e) There is no other method for doing addition and subtraction of complex number it is similar as like real number