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Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters. If your answer includes a number that is not an integer type it as a decimal rounded to the nearest hundredth. \frac{2+3i}{2-3i}simplifies to a+bi where:a= Answerb= Answer

Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters. If your a class=

Answer :

Given:

[tex]\frac{2+3i}{2-3i}[/tex]

Simplify,

[tex]\begin{gathered} \frac{2+3i}{2-3i} \\ \text{Apply complex arithmatic rule,} \\ \frac{2+3i}{2-3i}=\frac{2+3i}{2-3i}\times\frac{2+3i}{2+3i} \\ =\frac{(2+3i)^2}{2^2-(3i)^2} \\ =\frac{2^2+2(6i)+(3i)^2}{4-(-9)} \\ =\frac{4+12i-9}{13} \\ =\frac{-5+12i}{13} \\ =-\frac{5}{13}+\frac{12}{13}i \end{gathered}[/tex]

The simplified form as a+bi is,

[tex]\begin{gathered} a=-\frac{5}{13} \\ b=\frac{12}{13} \end{gathered}[/tex]

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