Question

rationalize. 3+4i/2-3i​

Answer 1

$\huge\bf{Given}$

$\sf{\frac{3+4i}{2-3i}}$

$\huge\bf{Explanation:-}$

$\sf{To\: simplify\:the\:fraction\:we\:required\:to\:have}\\{\sf{\:a\:rational\:denominator.}}$

$\small\sf{This\: is\:achieved\:by\:multiplying\: the\: Numerator\:or\:}\\{\sf{ denominator\:by\:the\:complex\:conjugate\:of}}\\{\sf{the\:complex\:number\:of\:the\:denominator}}$

$\small\bf{\:The\:conjugate\:of\: (2-3i)\:is\:(2+3i)}$

• $\large\bf{\frac{3+4i}{2-3i}={\frac{(3+4i)(2+3i)}{(2-3i)(2+3i)}}}$

$\sf{Distributing\: the\: numerator\:and\: denominator}\\{\sf{using\:the\:FOIL\:method}}$

• $\large\bf{\frac{6+9i+8i+12i^{2}}{4+6i-6i-9i^{2}}}$

$\small\bf{\boxed{Reminder\:i^{2}=\sqrt{-1}=\:-1}}$

• $\large\bf{\frac{6+17i+12(-1)}{4+\cancel6i-\cancel6i-9(-1)}}$

• $\large\bf{\frac{6+17i-12}{4+9}}$

• $\large\bf{\frac{-6+17i}{13}}$

$\bold{\small}\rm{Expressing\: in\: standard\:form }$

• $\large\bf{\boxed{\frac{-6}{13}+{\frac{17}{13}i}{\:\:\:\:\:Answer}}}$

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➣$\bold{\small}\bf{Hope\:It\:Help\:You}$

➣$\bold{\small}\bf{Be\:Brainly}$