Simplify 5i-6x=(10y)i+2

Question

Simplify

I need to know how to simplify this number

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5i-6x=(10y)i+2

Answer 1

The goal is to solve for y in terms of x and establishing a real and imaginary. First you must get all imaginary values on the same side of the equation,

5i-6x=(10y)i+2

+ 6x

5i = 10yi + 2 + 6x

-10yi -10yi Subtract 10i on both sides

5i -10yi = 6x + 2 Now Factor out 5i

5i(1-2y) = 6x+2 Divide 5i on both sides

5i 5i

1-2y = 6x+2 * 5i Rationalize the denominator by multiplying 5i/5i

5i 5i

1-2y = 30xi+10i Subtract 1 on both sides

-25

-1 -1

-2y = 30xi+10i -1 FInd LCD which is -25

-25

-1 * -2y = 30xi + 10i + 25 *-1

2 -25 2 Multiply by negative one half on both sides

y= 30xi + 10i + 25 Factor out 5 from the numerator

50

y= 5(6xi + 2i + 5) Simplify

50

y= 6xi + 2i + 5 factor out 2i for imaginary part

10

y= 2i(x + 1) + 5 Simplify

10

y= (x+1)i + 1 Done

5 2