This question is based on the concept of polar form.Therefore, the expression in polar form is [tex]\bold {z = \sqrt{10(cos108.43\; + \; i \; sin108.43)}}[/tex]
Given the following complex numbers in:
w = 2(cos(90°) + i sin (90°))
As we know that,
sin 90 degree = 1
cos 90 degree = 0
Put these values in given equation,
We get,
w = 2(0+i(1))
w = 2(0)+2i
w = 0+2i
Hence the value of w in rectangular form is 0+2i .
Now solving 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
Therefore, the value of z in rectangular coordinate is -1+ 1i.
Now solving 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
= tan^-1(-3)
= -71.56
[tex]\Theta[/tex] = 180 - 71.56
[tex]\Theta[/tex] = 108.43
Therefore, the expression in polar form is,[tex]\bold{z = \sqrt{10(cos108.43\; + \; i \; sin108.43)}}[/tex]
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