Question

check each true statement about the number.
$7-\sqrt{3}i$
□ 7 is the real part of the number.
□ $\sqrt{3}$ is the imaginary part of the number.
□ $7-\sqrt{3}$ is the coefficient of $i$.
□ this number is the sum of a real number and an imaginary number.
done

Explanation:

Step1: Recall complex number form

A complex number is written as $a + bi$, where $a$ is the real part, and $b$ (the coefficient of $i$) is the imaginary part. For $7 - \sqrt{3}i$, this is equivalent to $7 + (-\sqrt{3})i$.

Step2: Evaluate first statement

Check if 7 is the real part.
In $7 + (-\sqrt{3})i$, $a=7$, so this is true.

Step3: Evaluate second statement

Check if $\sqrt{3}$ is the imaginary part.
The imaginary part is $-\sqrt{3}$, not $\sqrt{3}$, so this is false.

Step4: Evaluate third statement

Check if $7-\sqrt{3}$ is the coefficient of $i$.
The coefficient of $i$ is $-\sqrt{3}$, not $7-\sqrt{3}$, so this is false.

Step5: Evaluate fourth statement

Check if the number is sum of real and imaginary number.
A complex number is the sum of real part $7$ (real number) and $-\sqrt{3}i$ (imaginary number), so this is true.

Answer:

• 7 is the real part of the number.
• This number is the sum of a real number and an imaginary number.