Mistake in expression

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

(2 - 5i)(5 + 2i) = 10 + 4i - 25i - 10i2
= 10 + 4(-1) - 25(-1) - 10(1)
= 10 - 4 + 25 - 10
= 21

Complete the explanation and correct the error.

Hint: The student incorrectly defined i as being equal to ___ instead of ___. The student should have written the product as :

Correct answer:

x = 20-21i

Step-by-step explanation:

$$\begin{gathered} x=(2-5i)\cdot (5+2i) \\ x=2\cdot 5+2\cdot 2i+(-5i)\cdot 5+(-5i)\cdot 2i \\ x=10+4i-25i-10i_2 \\ x=10+4i-25i+10 \\ x=10+10+i(4-25) \\ x=20-21i \end{gathered}$$

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