Answer:
In rectangular form, z - w = 1 - 1i
Step-by-step explanation:
Got it correct on Edge 2020
In rectangular form, (z − w = 1 - i) and in polar form [tex]\rm z-w = \sqrt{2} (cos135^\circ+isin135^\circ)[/tex] and this can be determined by using the given data.
Given :
First, evaluate the value of 'z' by using the below calculation.
[tex]\rm z=\sqrt{2} (cos45^\circ+i\;sin45^\circ)[/tex]
[tex]\rm z=\sqrt{2} (\dfrac{1}{\sqrt{2} }+i\dfrac{1}{\sqrt{2} })[/tex]
z = 1 + i     --- (1)
Now, evaluate the value of 'w' by using the below calculation.
[tex]\rm w={2} (cos90^\circ+i\;sin90^\circ)[/tex]
[tex]\rm w={2} (0+i)[/tex]
w = 2i   ---- (2)
Now, the difference (z - w) is given by:
z - w = 1 + i - 2i
z - w = 1 - i
The rectangular form of (z - w) is given by:
z - w = 1 - i
Now, the modulus of (z - w) is given by:
[tex]\rm |z - w| = \sqrt{1^2+(-1)^2}[/tex]
[tex]\rm |z-w| = \sqrt{2}[/tex]
Now, the argument is given by:
[tex]\rm \theta = tan^{-1}\dfrac{y}{x}\\[/tex]
[tex]\rm \theta = -45^\circ[/tex]
[tex]\theta = 180-45 = 135^\circ[/tex]
The polar form of (z - w) is given by:
[tex]\rm z-w=|z-w|(cos\theta-i \; sin\theta)[/tex]
[tex]\rm z-w = \sqrt{2} (cos135^\circ+isin135^\circ)[/tex]
For more information, refer to the link given below:
https://brainly.com/question/11657509
