Question

Z=sqrt 2[cos(-pi/4)+isin(-pi/4)]=a+bi what is a and b?

Answer 1

Answer: a=1, b=-1

Step-by-step explanation: I got this right on Edmentum

Answer 2

`\boxed{\boxed{a=1,b=-1}}`

Explanation:

The given expression is,

`z=√(2)\left[\cos(-(\pi)/(4))+i\sin (-(\pi)/(4))\right]`

According to Distributive property,

`=√(2)\cos(-(\pi)/(4))+i√(2)\sin (-(\pi)/(4))`

we know that,

`\cos(-(\pi)/(4))=\cos((\pi)/(4))=(1)/(\sqrt2)`

and

`\sin(-(\pi)/(4))=-\sin((\pi)/(4))=-(1)/(\sqrt2)`

Putting these,

`=√(2)\cdot (1)/(\sqrt2)-i√(2)\cdot (1)/(\sqrt2)`

`=1-i\cdot 1`

`=1-i`

Comparing this to
`a+bi`, we get

`a=1,b=-1`