Solve 1text{giga}=10^3

$$1 \text { giga } = 10 ^ { 3 }$$

Solve for a

$$a=\frac{-1000i}{g^{2}}$$

$$g\neq 0$$

Steps for Solving Linear Equation

Multiply g and g to get g^{2}.

$$1g^{2}ia=10^{3}$$

Multiply 1 and i to get i.

$$ig^{2}a=10^{3}$$

Calculate 10 to the power of 3 and get 1000.

$$ig^{2}a=1000$$

Divide both sides by ig^{2}.

$$\frac{ig^{2}a}{ig^{2}}=\frac{1000}{ig^{2}}$$

Dividing by ig^{2} undoes the multiplication by ig^{2}.

$$a=\frac{1000}{ig^{2}}$$

Divide 1000 by ig^{2}.

$$a=\frac{-1000i}{g^{2}}$$

Solve for g

$$g=\sqrt{5}\left(-10+10i\right)a^{-\frac{1}{2}}$$

$$g=\sqrt{5}\left(10-10i\right)a^{-\frac{1}{2}}\text{, }a\neq 0$$