Question

If x=1+3i ,y=x-i find the value of x^2-y^2​

Answer 1

Explanation:

x = 1 + 3i

x^2 = (1 + 3i)(1 + 3i)

• f: 1 * 1 = 1
• o: 1 * 3i = 3i
• i: 3i * 1 = 31
• L: = 3i * 3i = 9i^2 = - 9

x^2 = 1 + 6i - 9 = -8 + 6i

By a similar method

y = (x - i)

y^2 = x^2 - 2i*x + i^2

y^2 = x^2 - 2ix - 1

y^2 = -8+6i - 2i(1 + 3i) -1

y^2 = -8+6i -2i - 6i - 1

y^2 = -8 - 2i - 1

y^2 = - 9 - 2i

x^2 - y^2 = -8 + 6i - (9 - 2i)

x^2 - y^2 = -8 + 6i - 9 + 2i

x^2 - y^2 = -17 + 8i