131 LearnersLast updated on May 26th, 2025
Square of -1
The product of multiplying an integer by itself is the square of a number. Squaring is used in programming, calculating areas, and various mathematical computations. In this topic, we will discuss the square of -1.
What is the Square of -1
The square of a number is the product of the number by itself. The square of -1 is -1 × -1. The square of a number always results in a positive number, except for the square of 0. We write it in math as (-1)², where -1 is the base and 2 is the exponent. The square of both positive and negative numbers is always positive. For example, 5² = 25; (-5)² = 25.
The square of -1 is -1 × -1 = 1.
Square of -1 in exponential form: (-1)²
Square of -1 in arithmetic form: -1 × -1
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How to Calculate the Value of Square of -1
The square of a number is found by multiplying the number by itself. Let’s learn how to find the square of a number. These are the common methods used to find the square of a number.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By the Multiplication method
In this method, we multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of -1.
Step 1: Identify the number. Here, the number is -1.
Step 2: Multiplying the number by itself, we get, -1 × -1 = 1. The square of -1 is 1.
Using a Formula (a²)
In this method, the formula, a², is used to find the square of the number. Where a is the number.
Step 1: Understanding the equation Square of a number = a²
a² = a × a
Step 2: Identifying the number and substituting the value in the equation.
Here, ‘a’ is -1. So: (-1)² = -1 × -1 = 1
By Using a Calculator
Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of -1.
Step 1: Enter the number in the calculator Enter -1 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is -1 × -1
Step 3: Press the equal to button to find the answer Here, the square of -1 is 1.
Tips and Tricks for the Square of -1: Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.
- The square of any real number is always non-negative.
- The square of an even number is always an even number. For example, 6² = 36.
- The square of an odd number is always an odd number. For example, 5² = 25.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
- The square of -1 is a special case and is used in complex numbers, where i² = -1.
Common Mistakes to Avoid When Calculating the Square of -1
Mistakes are common among students when doing math, especially when it involves finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip steps or swap digits. To avoid this, students should double-check their answers. They can double-check by finding the square root of the solution they found. For example, the square of 25 is 625, and the square root of 625 is ±25.
Mistake 2
Errors when using the formula.
The formula to find the square of a number is a². Instead, students may incorrectly apply operations, such as (-1)² with (-1 + 1)². So, students should check and use the correct formula and double-check the answers to avoid all confusion.
Mistake 3
Confusing with square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid this, students should understand the concept that square and square root are inverse operations. The square of 5 is 25, and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses and perform operations in the correct order to avoid errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should practice regularly to avoid errors.
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Solved Examples on Square of -1
Problem 1
Find the result of multiplying -1 by itself.
The result of multiplying -1 by itself is 1.
Explanation
The square of -1 is -1 × -1 = 1.
Problem 2
A complex number has a real part of 0 and an imaginary part of -1. What is the square of this number?
The square of the complex number 0 - 1i is -1.
Explanation
The square of the imaginary unit i is -1, so (-1i)² = -1² × i² = 1 × (-1) = -1.
Problem 3
In physics, negative resistance is represented by -1. Calculate the square of the resistance.
The square of the resistance is 1.
Explanation
Resistance squared: (-1)² = -1 × -1 = 1.
Problem 4
A physical quantity is represented as -1. What is its square?
The square of the quantity is 1.
Explanation
The square of -1 is -1 × -1 = 1.
Problem 5
If a vector has a magnitude of -1, what is the square of its magnitude?
The square of the magnitude is 1.
Explanation
The square of a magnitude represented by -1 is (-1)² = 1.
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FAQs on Square of -1
1.What is the square of -1?
2.What is the square root of -1?
3.Is -1 a prime number?
4.How does the square of -1 relate to complex numbers?
5.What does the square of -1 represent in mathematics?
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Important Glossaries for Square of -1.
- Imaginary unit: The imaginary unit is denoted as i, where i² = -1.
- Complex number: A complex number is a number that comprises a real and an imaginary part, such as a + bi.
- Square: The square of a number is the product of multiplying the number by itself.
- Square root: The square root is the inverse operation of squaring a number.
- Exponential form: Exponential form is the way of writing a number in the form of a power, such as a² where a is the base.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
