Factor the expression over the set of complex numbers $4 a ^ { 2 } + 9$
A) $\quad ( 2 + 3 i ) ( 2 - 3 i )$
B) $\quad ( 2 a + 3 ) ( 2 a - 3 )$
C) $\quad ( - 2 a + 3 i ) ( - 2 a + 3 i )$
D) $\quad ( 2 a + 3 i ) ( 2 a - 3 i )$
E) $\quad ( 2 a + 3 i ) ( 2 a + 3 i )$

Question

Quizplus · Accepted Answer

We can factor the expression using the difference of squares formula: $$4a^{2}+9=(2a)^{2}+(3i)^{2}=(2a+3i)(2a-3i)$$ Note that in the complex numbers, $i^{2}=-1$, so we can rewrite our expression as a sum of squares. The only answer choice that matches this factorization is D.

Factor the Expression Over the Set of Complex Numbers 4a2+94 a ^ { 2 } + 94a2+9

Factor the Expression Over the Set of Complex Numbers $4 a ^ { 2 } + 9$