Perform the operation and write the result in standard form. $$( 4 + 9 i ) ^ { 2 }$$
A) $16 + 81 i$
B) $97 - 8 i$
C) $- 65 + 72 i$
D) $- 8 + 18 i$
E) $16 - 9 i$

Question

Quizplus · Accepted Answer

To solve $(4 + 9i)^2$, we expand it as $(4 + 9i)(4 + 9i)$. Using the distributive property (FOIL method), we get $4^2 + 2(4)(9i) + (9i)^2 = 16 + 72i - 81$, because $i^2 = -1$. Simplifying, we get $-65 + 72i$.

Perform the Operation and Write the Result in Standard Form (4+9i)2( 4 + 9 i ) ^ { 2 }(4+9i)2

Perform the Operation and Write the Result in Standard Form $( 4 + 9 i ) ^ { 2 }$