Solve z_{3}=(2+j)(3-5j)

$$z _ { 3 } = ( 2 + j ) ( 3 - 5 j )$$

Solve for z_3

$$z_{3}=\left(3-5j\right)\left(j+2\right)$$

Solution Steps

Use the distributive property to multiply 2+j by 3-5j and combine like terms.

$$z_{3}=6-7j-5j^{2}$$

Solve for j

$$j=\frac{\sqrt{169-20z_{3}}-7}{10}$$

$$j=\frac{-\sqrt{169-20z_{3}}-7}{10}\text{, }z_{3}\leq \frac{169}{20}$$