Consider the numbers z= sqr2 (cos 45º + i sin 45° )and w = 2(cos 90° + i sin 90).

Fill in the blanks to complete the statements.

In rectangular form, z - w = 1 - i

In polar form z-w=

= sqr2 (cos + i sin )

Answer:

RECTANGULAR FORM: z -w = 1- 1i

POLAR FORM: z-w = √2(cos135°+i sin135°)

Step-by-step explanation:

Find the image attached

Given the following complex numbers

z = √2 (cos 45º + i sin 45° )

w = 2(cos 90° + i sin 90).

The complex number in rectangular form is expressed as z = x+iy

(x, y) are the rectangular coordinates

Given

z = √2 (cos 45º + i sin 45° )

z = √2 (1/√2+ ( 1/√2)i )

z =  √2(1/√2) +  √2(1/√2)i

z = 1 + i .... 1

Also;

w = 2(cos 90° + i sin 90)

w = 2(0 + 1i)

w  = 2(0) + 2i

w = 0+2i ....2

Take their difference:

z - w = 1 + i - (0+2i)

z-w = 1+i-0-2i

z-w = 1-0+i-2i

z-w = 1-i

Hence the values that goes into the box is 1.

z-w = 1 - 1i

In Polar form;

Get the modulus of the resulting complex number:

|z-w| = √1²+1²

|z-w| = √2

Get the argument:

[tex]\theta = tan^{-1}\frac{y}{x} \\\theta = tan^{-1}(\frac{-1}{1}) \\\theta = tan^{-1}(-1) \\\theta = -45^0[/tex]

Since tan is negative in the second quadrant, the angle will be 180-45 = 135°

The polar form of the complex umber is expressed as;

z-w = |z-w|(cosθ-isinθ)

z-w = √2(cos135°+i sin135°)

Answer: 1, 315, 315

Step-by-step explanation: right on edge

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