Question

2x+i^9y(2+i)=xi^7+10i^16​

Answer 1

it is given that, 2x + i^9y(2 + i) = xi^7 + 10i^16

we know, i = √(-1) ⇒i² = -1

so, i³ = i²i = -i

or, (i^9) = (i³)³ = (-i)³ = -i³ = -(-i) = i

also i^16 = (i⁴)⁴ = (1)⁴ = 1

and i^7 = i (i²)³ = i × (-1) = -i

now, 2x + i y(2 + i) = x(-i) + 10(1)

or, 2x + y(2i + i²) = -xi + 10

or, 2x + y(2i - 1) = -xi + 10

or, 2x + 2yi - y = -xi + 10

or, (2x - y - 10) + (2y + x)i = 0

so, 2x - y - 10 = 0... .(1)

and (2y + x) = 0....... (2)

from equations (1) and (2),

y = -2 and x = 4

Answer 2

Answer:

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