Question

Solve the equation for x, y ∈ R
2x + i⁹y (2 + i) = xi⁷ + 10i¹⁶

Answer 1

Answer:

x = 4

y = -2

Step-by-step explanation:

Concept:

$i^{4n}=1\\\\i^{4n-3}= i\\\\i^{4n-2}=-1\\\\i^{4n-1}=-i$

Given:

$2x+i^9y(2+i)=x\:i^7+10\:i^{16}$

2x+iy(2+i)=-xi+10

(2x-y)+i2y = 10 - ix

separating real and imaginary parts

2x - y = 10.......(1)

2y = -x

x= -2y...........(2)

using (2) in (1)

2(-2y) - y = 10

- 4y - y = 10

-5y = 10

y = -2

x= 4