contestada

[tex]\frac{8-i}{3-2i}[/tex] If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: [tex]i=\sqrt{-1}[/tex]

Respuesta :

ujalakhan18

Answer:

a = 2 , b = 1

Step-by-step explanation:

[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]

=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]

=> [tex]\frac{24+13i-2i^2}{13}[/tex]

=> [tex]\frac{26+13i}{13}[/tex]

Comparing it with a+bi

a = 26/13 , b = 13/13

a = 2, b = 1

09pqr4sT

Answer:

a = 2

b = 1

Step-by-step explanation:

[tex]\frac{8-i}{3-2i}[/tex]

Write the fraction in this form:

[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]

[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]

Evaluate.

[tex]\frac{26+13i}{13}[/tex]

Factor the numerator.

[tex]\frac{13\left(2+i\right)}{13}[/tex]

[tex]2+1i[/tex]

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