Question

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

Question 10 options:

A)

–153∕4 + 4i

B)

153∕4 + 8i

C)

–153∕4 + 8i

D)

153∕4 + 4i

Answer 1

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

Answer:

`= ( - 63)/(4) + 4i`

Explanation:

we must know that

• (a + b)² = a² + b² + 2ab

`{( (1)/(2) + 4i) }^(2) = { ((1)/(2) })^(2) + {(4i)}^(2) + 2 . (1)/(2) . 4i`

`= (1)/(4) + 16 {i}^(2) + 4i`

• since i²= -1

`= (1)/(4) - 16 + 4i`

`= (1 - 64)/(4) + 4i`

`= \underline{ ( - 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

Explanation:

153∕4 + 8i is the correct answer