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Find the values of x and y which satisfy the following equations (x, y ∈ R), 

If x + 2i + 15i6 y = 7x + i3 (y + 4), find x + y

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Best answer

x + 2i + 15i6 y = 7x + i3(y + 4)

x + 2i + 15(i2)3 y = 7x + i3(y + 4)

x + 2i + 15(-1)3 y = 7x – i(y + 4) ……[∵ i2 = -1, i3 = -i] 

x + 2i – 15y – 7x + iy + 4i = 0

(-6x – 15y) + i(y + 6) = 0 + 0i

Equating real and imaginary parts, we get

-6x – 15y = 0 and y + 6 = 0

-6x – 15y = 0 and y = -6

-6x – 15(-6) = 0

-6x + 90 = 0

∴ x = 15

∴ x + y = 15 – 6 = 9

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