Question

9. Find the exact values of x and y such that (x + yi)² - (x-yi)² = x -y + 16i.

Answer 1

x = 5.3333...

y = 3.2

btw my discord is Bandu#0789

Explanation:

(x + yi)² - (x - yi)² = x - y + 16i

x² + 2xyi + y²i² - (x² - 2xyi + y²i²) = x - y + 16i

x² + 2xyi + y²i² - x² + 2xyi - y²i² = x - y + 16i

2xyi + y²i² + 2xyi - y²i² = x - y + 16i

4xyi + y²i² - y²i² = x - y + 16i

4xyi = x - y + 16i

4xyi/x = (x - y + 16i)/x

4yi = -y + 16i

4yi/i = (-y + 16i)/i

4y = -y + 16

4y/4 = (-y + 16)/4

y = -y/4 + 4

y - 4 = -y/4

-4 = -y/4 - y

-16/4 = -y/4 - 4y/4

-16/4 = -5y/4

-16/4 × 4 = -5y/4 × 4

-16 = -5y

-16/-5 = -5y/-5

y = 3.2

4xyi = x - y + 16i

4xyi/y = (x - y + 16i)/y

4xi = x + 16i

4xi/i = (x + 16i)/i

4x = x + 16

4x - x = x - x + 16

3x = 16

3x/3 = 16/3

x = 5.33333...