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

Answer:

a = 1

b = - 1

Explanation:

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

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

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:

$\begin{gathered} z=\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}-\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}i \\ z=\frac{2}{2}-\frac{2}{2}i \\ z=1-1i \end{gathered}$

Therefore, we can complete the equation as:

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

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