Question

If x =-1+i then find x3-6x2+2x-1

Answer 1

Answer:

16i - 1

Solution:

• Given : x = -1 + i
• To find : x³ - 6x² + 2x - 1

We have ;

=> x = -1 + 1

=> x + 1 = i

=> (x + 1)² = i² { squaring both sides }

=> x² + 2x + 1 = -1

=> x² + 2x + 1 + 1 = 0

=> x² + 2x + 2 = 0

Now,

Let's divide x³ - 6x² + 2x - 1 by x² + 2x + 2 .

Thus,

Here we go ↓

x² + 2x + 2 ) x³ - 6x² + 2x - 1 ( x - 8

x³ + 2x² + 2x

– – –

– 8x² – 1

– 8x² – 16x – 16

+ + +

16x + 15

Here,

Dividend = x³ - 6x² + 2x - 1

Divisor = x² + 2x + 2

Quotient = x - 8

Remainder = 16x + 15

Also,

We know that ;

Dividend = Divisor × Quotient + Remainder

Thus,

x³- 6x²+ 2x -1 = (x²+ 2x+ 2)×(x - 8) + 16x +15

= 0×(x - 8) + 16x + 15

= 0 + 16(-1 + i) + 15

= -16 + 16i + 15

= 16i - 1

Hence,

x³ - 6x² + 2x - 1 = 16i - 1