Answer:
[tex]\frac{-2+i}{-4-5i} = \frac{3}{41}-i\frac{14}{41}[/tex]
Step-by-step explanation:
[tex]\frac{-2+i}{-4-5i}[/tex]
Apply complex arithmetic rule: [tex]\frac{a + bi}{c + di} = \frac{(c-di) (a + bi)}{(c-di) (c + di)} =\frac{(ac+bd)+(bc-ad)i}{c^2+d^2}[/tex]
[tex]a=-2,b=1, c=-4,d=-5[/tex]
[tex]=\frac{\left(-2\left(-4\right)+1\cdot \left(-5\right)\right)+\left(1\cdot \left(-4\right)-\left(-2\right)\left(-5\right)\right)i}{\left(-4\right)^2+\left(-5\right)^2}[/tex]
Refine:
[tex]=\frac{3-14i}{41}[/tex]
Rewrite [tex]\frac{3-14i}{41}[/tex] in standard complex form: [tex]\frac{3}{41} - \frac{14}{41}i[/tex]
Final answer: [tex]\frac{3}{41} - \frac{14}{41}i[/tex]
Hope I helped! If so, may I get Brainliest and a Thanks?
Thank you, Have a good one! =)
