martinezadam576
Answered

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Select the correct answer.

Subtract [tex][tex]$8 + 7i$[/tex][/tex] from [tex][tex]$4 - 16i$[/tex][/tex]:

A. [tex][tex]$4 - 23i$[/tex][/tex]
B. [tex][tex]$4 - 11i$[/tex][/tex]
C. [tex][tex]$4 + 9i$[/tex][/tex]
D. [tex][tex]$-4 - 23i$[/tex][/tex]

Sagot :

GinnyAnswer
To find the result of subtracting [tex]\( 8 + 7i \)[/tex] from [tex]\( 4 - 16i \)[/tex], follow these steps:

1. Write down the complex numbers:
[tex]\[ a = 4 - 16i \][/tex]
[tex]\[ b = 8 + 7i \][/tex]

2. Subtract the second complex number from the first:
[tex]\[ (4 - 16i) - (8 + 7i) \][/tex]

3. Separate the real parts and the imaginary parts:
[tex]\[ (4 - 8) + (-16i - 7i) \][/tex]

4. Perform the arithmetic for the real parts:
[tex]\[ 4 - 8 = -4 \][/tex]

5. Perform the arithmetic for the imaginary parts:
[tex]\[ -16i - 7i = -23i \][/tex]

6. Combine the results:
[tex]\[ -4 - 23i \][/tex]

Therefore, the result of the subtraction is [tex]\( -4 - 23i \)[/tex].

The correct answer is:
D. [tex]\(-4 - 23i\)[/tex]
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