Question

Select the correct answer from each drop-down menu.if z=pi2[cos(-pi/4)+isin(-pi/4)] =a+bi , in rectangular form, then a= ____ and b= _____

Answer 1

a = 1

b = - 1

Step-by-step explanation:

To know the values of a and b, we need to solve the following equation:

`z=\sqrt[]{2}\lbrack\cos ((-\pi)/(4))+i\sin ((-\pi)/(4))\rbrack`

So, replacing cos(-π/4) by √2/2 and sin(-π/4) by -√2/2, we get:

`z=\sqrt[]{2}\cdot(\frac{\sqrt[]{2}}{2}+i\frac{-\sqrt[]{2}}{2})`

Applying the distributive property:

`\begin{gathered} z=\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}-\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}i \\ z=(2)/(2)-(2)/(2)i \\ z=1-1i \end{gathered}`

Therefore, we can complete the equation as:

`z=1-1i=a+bi_{}`

It means that a = 1 and b = - 1.