Solve h = m/(2 + m); m = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$h=\frac{m}{2+m}; m=$$

Solve for h, m

$h=\frac{1}{5}+\frac{2}{5}i=0.2+0.4i$
$m=i$

Solution Steps

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$m=i$$

Consider the first equation. Insert the known values of variables into the equation.

$$h=\frac{i}{2+i}$$

Multiply both numerator and denominator of $\frac{i}{2+i}$ by the complex conjugate of the denominator, $2-i$.

$$h=\frac{i\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}$$

Do the multiplications in $\frac{i\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}$.

$$h=\frac{1+2i}{5}$$

Divide $1+2i$ by $5$ to get $\frac{1}{5}+\frac{2}{5}i$.

$$h=\frac{1}{5}+\frac{2}{5}i$$

The system is now solved.

$$h=\frac{1}{5}+\frac{2}{5}i$$ $$m=i$$