If (x+yi) (1-3i) = 10

Then x+y=

x + y = 4

Step-by-step explanation:

Given that, (x + iy) (1 - 3i) = 10, then we have to calculate x + y.

Now, (x + iy) (1 - 3i) = 10

⇒ x (1 - 3i) + iy (1 - 3i) = 10

⇒ x - 3xi + iy - 3yi² = 10

⇒ (x + 3y) + i (y - 3x) = 10

Now, comparing the real and imaginary part of both sides we get,

(x + 3y) = 10 ... (1) and

y - 3x = 0

⇒ y = 3x ... (2)

Solving equations (1) and (2) we get

x + 3 (3x) = 10

⇒ x = 1

So, y = 3x = 3

Therefore, x + y = 1 + 3 = 4 (Answer)