Question

Prove that

[(3+2i)/(2-5i)+(3-2i)/(2+5i)] is rational

Answer 1

Answer:

(3+2i) (2+5i) + (3-2i) (2-5i)

(2-5i) (2?+5i)

6+15i +4i +10i + 6-15i -4i + 10i

(2) -(5i)

6+6 - 10 - 10 /4- 25i =-8/4+25 = -8/29

Answer 2

Answer:

Rational expression of the given value is = -8/29 .

Step-by-step explanation:

Determine the proving of the rational expression.

(3 + 2i)/(2 - 5i) + (3 - 2i)/(2 + 5i) =

((3 + 2i)(2 + 5i) + (3 - 2i)(2 - 5i))/((2 - 5i)(2 + 5i))

Therefore   a ^ 2 - b ^ 2 = (a + b)(a - b)

= (6 + 15i + 4i + 10i ^ 2 + 6 - 15i - 4i + 10i ^ 2)/(2 ^ 2 - (5i) ^ 2) i ^ 2

= - 1

=(6 + 15i + 4i + 10(- 1) + 6 - 15i - 4i + 10(- 1))/(4 - 25(- 1))

=(6 + 19i - 10 + 6 - 19i - 10)/(4 + 25)

=(12 - 20)/29 =- 8/29

Hence, the rational expression of the given value is = -8/29 .

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