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Substitute 5+2i into the given equation. Recall the definition of the imaginary unit i.
Yes, see solution.
We want to determine whether 5+2i is a solution to the given equation. To do so, we can substitute x=5+2i into the equation. If we receive a true statement, then it is indeed a solution. Before we do that, recall that the imaginary unit i is the complex number whose square is - 1.
x= 5+2i
(a+b)^2=a^2+2ab+b^2
Calculate power
Multiply
(a b)^m=a^m b^m
Calculate power
i^2=- 1
a(- b)=- a * b
Subtract term
Distribute -10
Subtract terms
Since the substitution of 5+2i resulted in a true statement, we know that it is indeed a solution to the given equation.