Question Video: Arithmetic with Imaginary Numbers Mathematics

What is the value of (5𝑖)²?

01:11

Video Transcript

What is the value of five 𝑖 squared?

We recall that an imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit 𝑖, which is defined by the property 𝑖 squared is equal to negative one.

In this question, we want to square the term five 𝑖. Squaring the real part gives us 25 as five squared or five multiplied by five is 25. Squaring the imaginary part, 𝑖 multiplied by 𝑖, gives us 𝑖 squared. As 𝑖 squared is equal to negative one, 25𝑖 squared is equal to 25 multiplied by negative one. Multiplying a positive number by a negative number gives a negative answer. Therefore, 25 multiplied by negative one is negative 25.

The value of five 𝑖 all squared is negative 25.

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