Question

While attempting to multiply the expression (2-5i)(5+2i) a student made a mistake.

(2-5i)(5+2i)= 10+4i -25i - 10i^2
=10+4(-1)-25(-1) - 10(1)
=10-4+25-10
=21
What is the error?

Answer 1

The left side of the equation is ignored

i is treated as -1, which it is not, it is instead the square root of negative 1.

To solve it properly we get:

(2 - 5i)(5 + 2i)

= 10 + 4i - 25i - 10i²

= 10 + 21i + 10

= 20 - 21i

Answer 2

The error is that, the student replaced i with -1 which is wrong as i = √-1

And he has replaced i^2 with 1 while i^2 = -1

Explanation:

Given two numbers that are being multiplied are:

(2-5i)(5+2i)

We will solve the question to get the right result so that the error can be detected.

So, multiplying both

`= 2(5+2i)-5i(5+2i)\\=10+4i-25i-10i^2\\=10-21i-10(-1)\ \ \ as\ i^2 = -1\\=10-21i+10`

The error is that, the student replaced i with -1 which is wrong as i = √-1

And he has replaced i^2 with 1 while i^2 = -1