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.

Explanation:

Step1: Recall Complex Number Form

A complex number is in the form \(a + bi\), where \(a\) is the real part, \(b\) is the coefficient of \(i\) (imaginary part), and \(bi\) is the imaginary number.

Step2: Analyze \(7 - \sqrt{3}i\)

• For "7 is the real part": The number is \(7 + (-\sqrt{3})i\), so real part \(a = 7\). This is true.
• For "\(\sqrt{3}\) is the imaginary part": The imaginary part (coefficient of \(i\)) is \(-\sqrt{3}\), not \(\sqrt{3}\). False.
• For "\(7 - \sqrt{3}\) is the coefficient of \(i\)": Coefficient of \(i\) is \(-\sqrt{3}\), not \(7 - \sqrt{3}\). False.
• For "Sum of real and imaginary number": \(7\) (real) and \(-\sqrt{3}i\) (imaginary), so it's their sum. True.

Answer:

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