Question

Write each of the following quadratic expressions as the product of two linear factors

a) z^2 + 4i
b) z^2 + 4
c) z^2 − 4
d) z^2 − 4i

Answer 1

Answer with Step-by-step explanation:

Since we have given quadratic expressions in the form of

`a^2-b^2`

which is equal to
`(a+b)(a-b)`

a) z^2 + 4i =
`(z-2i√(i))(z+2i√(i))`

b) z^2 + 4 =
`(z-2i)(z+2i)`

c) z^2 − 4 =
`(z-2)(z+2)`

d) z^2 − 4i =
`(z+2√(i))(z-2√(i))`

Since a) and b) contains complex number so, it splits into complex linear factors.