Imagenary unit

Algebra Level 2

( 7 i − 5 ) ( 8 i − 5 ) = ? \large (7i-5)(8i-5)=?

− 21 − 90 i -21-90i − 21 − 100 i -21-100i − 31 − 40 i -31-40i − 31 − 35 i -31-35i − 31 − 75 i -31-75i

Matin Naseri by Matin Naseri , 17, Afghanistan

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1 solution

Munem Shahriar
Aug 24, 2018

( 7 i − 5 ) ( 8 i − 5 ) = 7 i ( 8 i − 5 ) − 5 ( 8 i − 5 ) = 56 i 2 − 35 i − 40 i + 25 = 56 ( − 1 ) − 75 i + 25 [ i 2 = − 1 ] = − 56 − 75 i + 25 = − 31 − 75 i \begin{aligned}(7i - 5)(8i - 5) & = 7i(8i - 5) - 5(8i - 5) \\ & = 56i^2 - 35i - 40i + 25 \\ & = 56(-1) -75i +25 ~~~ [i^2 = -1] \\ & = -56 -75i+25 \\ & = -31 - 75i \\ \end{aligned}

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