express $\dfrac{30+19i}{4+9i}$ in the form $a + bi$, where $a$ and $b$ are real numbers.
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Answered by
7
( 30 + 19i )/( 4 + 9i)
multiply ( 4 -9i) with numerator and denominator
= (30 + 19i)(4 - 9i)/(4 + 9i)(4 - 9i)
={ 30( 4 -9i) +19i(4 - 9i)}/{4² -(9i)²}
={ 120 -270i + 76i -171(i²)}/{16 - 81(i²)}
we know ,
i² = -1 use this here,
={ 120 -194i +171 }/{ 16 + 81}
= ( 291 - 194i)/97
= (291/97) - (194/97)i
hence, (291/97) + (-194/97)i is in the form of a + bi
multiply ( 4 -9i) with numerator and denominator
= (30 + 19i)(4 - 9i)/(4 + 9i)(4 - 9i)
={ 30( 4 -9i) +19i(4 - 9i)}/{4² -(9i)²}
={ 120 -270i + 76i -171(i²)}/{16 - 81(i²)}
we know ,
i² = -1 use this here,
={ 120 -194i +171 }/{ 16 + 81}
= ( 291 - 194i)/97
= (291/97) - (194/97)i
hence, (291/97) + (-194/97)i is in the form of a + bi
rishilaugh:
thanks abhi
:-)
Answered by
3
Answer:
multiply top/bottm by 4 - 9i
[ 30 + 19i ] [ 4 - 9i ] / ( 4 + 9i) (4 - 9i) ]
[ 120 + 76i - 270i - 171i^2 ] / [ 16 - 81i^2 ]
[ 120 + 171 - 194i ] / [ 16 + 81 ]
[ 291 - 194i ] / [ 97 ]
(291/ 97) - (194/97) i
3 - 2i
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