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# Can somebody explain complex number to me? For example these kinds of problems: Is 5i a solution to 6= x(squared) +23

Mar 8, 2018

$\text{See explanation}$

#### Explanation:

$i \text{ is a number with the property that } {i}^{2} = - 1.$
$\text{So if you fill in "5i", you will get}$
${\left(5 i\right)}^{2} + 23 = 25 {i}^{2} + 23 = 25 \cdot - 1 + 23 = - 2 \ne 6$
$\text{So "5 i" is not a solution.}$
$\text{Adding and multiplying with "i" goes just like with normal}$
$\text{real numbers, you just need to remember that } {i}^{2} = - 1.$
$\text{An odd power of "i" cannot be converted to a real number :}$
"(5 i)^3 = 125 * i^3 = 125 * i^2 * i = 125 * -1 * i = -125 i.
$\text{So then the imaginary unit "i" remains.}$