Question

Complete each statement given w = 2(cos(90o) + i sin (90o)) and z = StartRoot 2 EndRoot (cos(225o) + i sin(225o)). In rectangular form, w = 0 + i. In rectangular form, z = – 1i. In rectangular form, w + z = –1 + i. In polar form w + z = StartRoot 2 EndRoot (cos(o) + i sin(o)

Answer 1

Answer:

See explanations below

Step-by-step explanation:

Given the following complex numbers in polar form:

w = 2(cos(90°) + i sin (90°))

sin 90 = 1

cos 90 = 0

Substitute into the formula:

w = 2(0+i(1))

w = 2(0)+2i

w = 0+2i

Hence the value of w in rectangular form is  0+2i

For z:

z =√2(cos(225°) + i sin(225°))

z = √2(-1/√2+ i (-1/√2))

z = -√2/√2 - √2(-1/√2)i

z = -1+ 1i

Hence the value of z in rectangular coordinate is -1+ 1i

For  w + z:

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

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

w+z = -1+3i

Write w+z in polar form

Get the modulus

|w+z| = √(-1)²+3²

|w+z| = √1+9

|w+z| =  √10

Get the modulus

theta = tan^-1(-3)

theta = -71.56

theta = 180 - 71.56

theta = 108.43

The expression in polar form is z = √10(cos108.43+isin108.43)

Answer 2

Answer:

In rectangular form, w = 0 + 2i.

In rectangular form, z = -1 -1i.

In rectangular form, w + z = –1 + 1i

In polar form w + z = sqrt 2 (cos(135) + i sin(135).

Step-by-step explanation:

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