Question

find the value of expression 2 x cube + 2 x square - 7 x + 72 when X equal to 3 + 5i upon 2​

Answer 1

Answer:

4

Step-by-step explanation:

x = ( 3 + 5i ) / 2

x² = ( 3² - 5² + 2×3×5i) / 4 = ( 9 - 25 + 30i ) / 4 = ( -16 + 30i ) / 4 = -4 + (15/2)i

2x² = -8 + 15i

2x³ = (2x)(2x²)/2 = ( 3 + 5i ) ( -8 + 15i ) / 2

     = ( ( 3×-8 - 5×15 ) + ( 3×15 + 5×-8 )i ) / 2

     = ( ( -24 - 75 ) + ( 45 - 40 )i ) / 2

     = ( -99 + 5i ) / 2

2x³ + 2x² - 7x + 72

= -99/2 + (5/2)i -8 + 15i - (21/2) - (35/2)i + 72

= ( ( -99 - 16 -21 + 144 ) + ( 5 + 30 - 35 )i ) / 2

= ( 8 + 0i ) / 2

= 4