Question

What is the absolute value of 7 + 12i?

Answer 1

The absolute value of 7 + 12i is √193 ≈ 14

Further explanation

There are many types of numbers in mathematics such as :

• Natural Numbers : 1 , 2 , 3 , 4 , 5 , . . .
• Whole Numbers : 0 , 1 , 2 , 3 , 5 , . . .
• Integers : . . . , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , . . .
• etc

Complex Number consist of Real Number and Imaginary Number and can be expressed as :

$Z = a + b ~ i$

The absolute value of complex number is also called Modulus and can be calculated using this formula :

$|Z| = \sqrt { a^2 + b^2 }$

Let us tackle the problem.

$Z = 7 + 12~i$

$\text {Modulus of Z} = | Z | = \sqrt{ 7^2 + 12^2 }$

$| Z | = \sqrt{ 193 }$

$| Z | \approx 14$

Learn more

• Complex Numbers : brainly.com/question/5056377
• Match Each Product of Complex Numbers : brainly.com/question/1514840
• Graph of The Complex Plane : brainly.com/question/10662770

Answer details

Grade: High School

Subject: Mathematics

Chapter: Complex Numbers

Keywords: Complex , Number , Real , Imaginary , Whole , Natural , Integers

Answer 2

I'm thinking by "absolute value", you mean the magnitude. That is, the magnitude is the size of the vector on the complex plane. We can use the Pythagorean Theorem to calculate that. You treat the real values as your "x", and the imaginary part as your "y".

sqrt(7^2 + 12^2)
sqrt(49 + 144)
sqrt(193)