Question

please prove this fast​

Answer 1

Answer:

2+3i/3-4i. × 3+4i/3+4i

6 +9i +8i - 12/9+16

(17i- 6)/25

17i/25-6/25

a=-6/25

b=-17/25

Answer 2

a = -6/25 & b = 17/25 if (2  +  3i) /(3 - 4i) = a + ib  

Step-by-step explanation:

(2  +  3i) /(3 - 4i) = a + ib  

LHS =(2  +  3i) /(3 - 4i)

= (2 + 3 i) (3 + 4i) / ( 3 - 4i)(3 + 4i)

= (6 + 12i² + 17i ) /( 9 - 16i²)

i² = -1

= (6 - 12 + 17i)/(9 + 16)

= (-6 + 17i)/26

= -6/25  +  17 i/25

Comparing With RHS a + ib  

a = -6/25

b = 17/25

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