Converting from Polar form to Cartesian Form I am just starting with complex numbers and vectors. The question is: 

Convert the following to Cartesian form. 
a) $8 \,\text{cis} \frac \pi4$

The formula given is:
$$z = x +yi = r\space(\cos\theta + i\sin\theta)$$
With $r=8$ and $\theta = \frac\pi4$, I did:
$$z=8\left(\cos\frac\pi4 + i \sin \frac\pi4\right)$$
$$z = 8(0.71 + i0.71)$&
$$z = 5.66 + i5.66$$
The answer they give in the answers section is:
$$z=4\sqrt2(1+i)$$
I know this is the same answer just written approximately. Is someone able to take me through how you get to $z=4\sqrt2(1+i)$ instead of $z = 5.66 + i5.66$?

Knowing the $\pi\over4$ family:
$$\cos \dfrac{\pi}{4} = \sin \dfrac{\pi}{4} = \dfrac{1}{\sqrt 2}$$
Then applying this result to $8\,\text{cis} \frac{\pi}{4}$:
$$z=8\left(\dfrac{1}{\sqrt 2} + i\dfrac{1}{\sqrt 2}\right) = 8\cdot \dfrac{1}{\sqrt 2}(1+i)$$
And then multiply:
$$8\cdot \dfrac{1}{\sqrt 2} = \dfrac{8\sqrt 2}{2}=4\sqrt2$$
$$8\cdot \dfrac{1}{\sqrt 2}(1+i) = 4\sqrt 2(1+i)$$
