Trigonometry Examples

$2 i - 5 = 1 - x - y i$

Step 1

Rewrite the equation as $1 - x - y i = 2 i - 5$ .

$1 - x - y i = 2 i - 5$

Step 2

Reorder $2 i$ and $- 5$ .

$1 - x - y i = - 5 + 2 i$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Subtract $1$ from both sides of the equation.

$- x - y i = - 5 + 2 i - 1$

Step 3.2

Add $y i$ to both sides of the equation.

$- x = - 5 + 2 i - 1 + y i$

Step 3.3

Subtract $1$ from $- 5$ .

$- x = - 6 + 2 i + y i$

Step 4

Divide each term in $- x = - 6 + 2 i + y i$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x = - 6 + 2 i + y i$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1} + \frac{2 i}{- 1} + \frac{y i}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1} + \frac{2 i}{- 1} + \frac{y i}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1} + \frac{2 i}{- 1} + \frac{y i}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $- 6$ by $- 1$ .

$x = 6 + \frac{2 i}{- 1} + \frac{y i}{- 1}$

Step 4.3.1.2

Move the negative one from the denominator of $\frac{2 i}{- 1}$ .

$x = 6 - 1 \cdot (2 i) + \frac{y i}{- 1}$

Step 4.3.1.3

Rewrite $- 1 \cdot (2 i)$ as $- (2 i)$ .

$x = 6 - (2 i) + \frac{y i}{- 1}$

Step 4.3.1.4

Multiply $2$ by $- 1$ .

$x = 6 - 2 i + \frac{y i}{- 1}$

Step 4.3.1.5

Move the negative one from the denominator of $\frac{y i}{- 1}$ .

$x = 6 - 2 i - 1 \cdot (y i)$

Step 4.3.1.6

Rewrite $- 1 \cdot (y i)$ as $- (y i)$ .

$x = 6 - 2 i - y i$