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)
The area is 25
a= 1/2bh
=1/2(10)(5)
=1/2(50)
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