Respuesta :

The value of a = 11

What is complex numbers ?

  • Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.
  • The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]

put values in the formula -

[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29

square both sides

[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

Learn more about complex number

brainly.com/question/28007020

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