Question

Multiply the complex numbers: (1∕2 + 4i)2

Answer 1

[I'm supposing that you have to find the value of (1/ 2 + 4i)²]

Answer:

$= \frac{ - 63}{4} + 4i$

Step-by-step explanation:

we must know that

• (a + b)² = a² + b² + 2ab

${( \frac{1}{2} + 4i) }^{2} = { (\frac{1}{2} })^{2} + {(4i)}^{2} + 2 . \frac{1}{2} . 4i$

$= \frac{1}{4} + 16 {i}^{2} + 4i$

• since i²= -1

$= \frac{1}{4} - 16 + 4i$

$= \frac{1 - 64}{4} + 4i$

$= \underline{ \frac{ - 63}{4} + 4i}$

[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]

so the answer is option A.

Answer 2

Step-by-step explanation:

153∕4 + 8i is the correct answer