Evaluate the following :

2x4 + 5x3 + 7x2 – x + 41, when x = - 2 - √3i


Given:


⇒ x=-2-i


⇒ 2x4+5x3+7x2-x+41


⇒ 2(-2-)4+5(-2-i)3+7(-2-i)2-(-2-i)+41


⇒ 2(24+4(2)3(i)+6(2)2(i)2+4(2)(i)3+(i)4)-5(23+3(2)2(i)+3(2)(i)2+(i)3)+7(22+2(2)(i)+(i)2)+2+i+41


⇒ 16+64i+144i2+48i3+18i4-40-60i-90i2-15i3+28+28i+21i2+i+43


We know that i2=-1


⇒ 127+33i+75i2+33i3+18i4


⇒ 127+33i+75(-1)+33(-1)(i)+18(-1)2


⇒ 70


∴ 2x4+5x3+7x2-x+41=70


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