Question

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

Answer 1

x + y = 4

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)