Answer:
[tex]\boxed{\boxed{a=1,b=-1}}[/tex]
Step-by-step explanation:
The given expression is,
[tex]z=\sqrt{2}\left[\cos(-\dfrac{\pi}{4})+i\sin (-\dfrac{\pi}{4})\right][/tex]
According to Distributive property,
[tex]=\sqrt{2}\cos(-\dfrac{\pi}{4})+i\sqrt{2}\sin (-\dfrac{\pi}{4})[/tex]
we know that,
[tex]\cos(-\dfrac{\pi}{4})=\cos(\dfrac{\pi}{4})=\dfrac{1}{\sqrt2}[/tex]
and
[tex]\sin(-\dfrac{\pi}{4})=-\sin(\dfrac{\pi}{4})=-\dfrac{1}{\sqrt2}[/tex]
Putting these,
[tex]=\sqrt{2}\cdot \dfrac{1}{\sqrt2}-i\sqrt{2}\cdot \dfrac{1}{\sqrt2}[/tex]
[tex]=1-i\cdot 1[/tex]
[tex]=1-i[/tex]
Comparing this to [tex]a+bi[/tex], we get
[tex]a=1,b=-1[/tex]
