Evaluate the expression (4 + 7i)(11 - 4i) and write the result in the form a + bi.
A) $72 + 61 i$
B) $44 + 77 i$
C) $61 + 72 i$
D) $- 61 - 72 i$
E) none of these

Question

Evaluate the expression (4 + 7i)(11 - 4i) and write the result in the form a + bi. 
A) $72 + 61 i$
B) $44 + 77 i$
C) $61 + 72 i$
D) $- 61 - 72 i$
E) none of these

Quizplus · Accepted Answer

To evaluate the expression $(4 + 7i)(11 - 4i)$, we use the distributive property (FOIL method) to multiply the complex numbers:$$ (4 + 7i)(11 - 4i) = 4(11) + 4(-4i) + 7i(11) + 7i(-4i) $$$$ = 44 - 16i + 77i - 28i^2 $$Since $i^2 = -1$, we substitute this value in:$$ = 44 - 16i + 77i + 28 $$$$ = 72 + 61i $$Therefore, the result in the form $a + bi$ is $72 + 61i$.

Evaluate the Expression (4 + 7i)(11 - 4i) and Write 72+61i72 + 61 i72+61i

Evaluate the Expression (4 + 7i)(11 - 4i) and Write $72 + 61 i$