Question

Hi, can you please help me solve this question part (e)?

Answer 1

Given the vector

`z=-3+4i`

Part A

The modulus can be found as follow

`\sqrt[]{(-3)^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5`

`|z|=5`

Part B.

The argument of z can be found as follow

`\begin{gathered} \tan \text{ }\emptyset=(4)/(3) \\ \emptyset=\tan ^(-1)((4)/(3)) \\ \emptyset=53.130^0 \end{gathered}`

Since it is in the second quadrant,

`\emptyset=180^0-53.130^0=126.870^0`

Part C

`w=(10+4i)/(z)`

`w=(10+4i)/(-3+4i)`

we will rationalize the denominator

`\begin{gathered} w=(10+4i)/(-3+4i)*(-3-4i)/(-3-4i) \\ \\ w=(10+4i)/(9+16)=(-30-12i-40i+16)/(25)=(-14-52i)/(25) \\ \\ w=(-14)/(25)-(52i)/(25) \\ \end{gathered}`