Solving [tex]\frac{4-5i}{2+3i}[/tex] we get [tex]-\frac{7}{13}-\frac{22i}{13}[/tex]
Option A is correct.
Step-by-step explanation:
We need to find the result of [tex]\frac{4-5i}{2+3i}[/tex]
We need to remove i from the denominator. For removing i Multiplying and dividing by 2-3i:
[tex]\frac{4-5i}{2+3i}*\frac{2-3i}{2-3i}[/tex]
Solving:
[tex]=\frac{4-5i*2-3i}{2+3i*2-3i}\\=\frac{4(2-3i)-5i*(2-3i)}{(2)^2-(3i)^2}\\=\frac{8-12i-10i+15i^2)}{4-9i^2}\\We\,\,i^2=-1\\=\frac{8-12i-10i+15(-1))}{4-9(-1)}\\=\frac{8-12i-10i-15}{4+9}\\=\frac{8-15-12i-10i}{13}\\=\frac{-7-22i}{13}\\=-\frac{7}{13}-\frac{22i}{13}[/tex]
So, solving [tex]\frac{4-5i}{2+3i}[/tex] we get [tex]-\frac{7}{13}-\frac{22i}{13}[/tex]
Option A is correct.
Keywords: Complex numbers
Learn more about Complex numbers at:
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brainly.com/question/10736268
- brainly.com/question/4678474
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