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 = $(z-2i\sqrt{i})(z+2i\sqrt{i})$

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

c) z^2 − 4 = $(z-2)(z+2)$

d) z^2 − 4i =  $(z+2\sqrt{i})(z-2\sqrt{i})$

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