Question

1. find the value of \\(sqrt{-100}\\)

a. -10i
b. 10i
c. 10
d. 100i

1. what is the standard form of a complex number?

a. a + b
b. bi + cx
c. a + bi
d. mx + b

Explanation:

Question 1:

Step1: Recall the imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So we can rewrite \( \sqrt{-100} \) as \( \sqrt{100 \times (-1)} \).

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), here we extend it for complex numbers), we have \( \sqrt{100\times(-1)}=\sqrt{100}\times\sqrt{-1} \).

Step3: Calculate the square roots

We know that \( \sqrt{100} = 10 \) and \( \sqrt{-1}=i \), so \( \sqrt{100}\times\sqrt{-1}=10\times i = 10i \).

The standard form of a complex number is defined as \( a + bi \), where \( a \) is the real part and \( bi \) is the imaginary part (\( a,b \) are real numbers and \( i=\sqrt{-1} \)). Option a is just a sum of two real numbers, option b has an extra \( x \) which is not part of the standard complex number form, and option d is the slope - intercept form of a linear equation, not related to complex numbers.

Answer:

b. 10\(i\)

Question 5: