Q18 of 53 Page 112

Find the number of non-zero integral solutions of the equation |1 – i|^x = 2^x

We have equation as:

|1-i|^x = 2^x

(√2)^x = 2^x

2^x/2 = 2^x

On equating powers, we get:

x = 2x

2x - x = 0

x = 0

Hence, for the given solution 0 is the only integral solution.

If (x + iy)³ – u + iv, then show that:

If α and β are different complex numbers with |β| = 1 , then find

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that:

(a² + b²) (c² + d²) (e² + f²) (g² + h²) = A² + B²

If , then find the least positive integral value of m.

Questions · 53

5. Complex numbers and quadratic equations

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10

Find the number of non-zero integral solutions of the equation |1 – i|x = 2x