Solve a^2+2j^2=5

$$a ^ { 2 } + 2 j ^ { 2 } = 5$$

Solve for a (complex solution)

$$a=-\sqrt{5-2j^{2}}$$

$$a=\sqrt{5-2j^{2}}$$

Solve for j (complex solution)

$$j=-\frac{\sqrt{10-2a^{2}}}{2}$$

$$j=\frac{\sqrt{10-2a^{2}}}{2}$$

Solve for a

$$a=\sqrt{5-2j^{2}}$$

$$a=-\sqrt{5-2j^{2}}\text{, }|j|\leq \frac{\sqrt{10}}{2}$$

Solve for j

$$j=\frac{\sqrt{10-2a^{2}}}{2}$$

$$j=-\frac{\sqrt{10-2a^{2}}}{2}\text{, }|a|\leq \sqrt{5}$$