What are x and y if (3x+2iy)-(y-2ix)-2x=3-2i ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have (3x+2iy)-(y-2ix)-2x=3-2i and we need to find x and y.

(3x + 2iy) -(y - 2ix) - 2x = 3 - 2i

=> 3x + 2iy - y + 2ix - 2x = 3 - 2i

=> x - y + 2i(x + y) = 3 - 2i

equate the real and imaginary coefficients

x - y = 3 and x + y = -1

adding the two

2x = 2

=> x = 1

y = -2

The solution is x = 1 and y = -2

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll remove the brackets from the left side and we'll combine the real parts and imaginary parts:

3x + 2iy - y + 2ix - 2x = 3 - 2i

(3x - y - 2x) + i(2y + 2x) = 3 - 2i

(x - y) + i(2x + 2y) = 3 - 2i

Comparing, we'll get:

x - y = 3 (1)

2x + 2y = -2

x + y = -1 (2)

We'll add (1) and (2):

x - y + x + y = 3 - 1

2x = 2

x = 1

x + y = -1 <=> 1 + y = -1 => y = -2

The requested values for x and y are: x = 1 and y = -2.

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