a) Given: z_{1}=6\angle30^{\circ} and z_{2}=4+5i What is the resultant of the given

William Boggs

William Boggs

Answered question

2022-01-16

a) Given:
z1=630 and z2=4+5i
What is the resultant of the given complex numbers? In rectangular form.
b) Convert i into polar form

Answer & Explanation

kalfswors0m

kalfswors0m

Beginner2022-01-17Added 24 answers

Step 1
a) Given: z1=630 and z2=4+5i
First express z1 in rectangular form.
z1=630 implies magnitude of z1=6 and argument of z1=30
Then,
z1=630
=6(cos30+isin30)
=6(32+i2)
=33+3i
Step 2
Now find the resultant of the given complex numbers as follows.
z1+z2=33+3i+4+5i
=(4+33)+8i
Therefore, the resultant of the given complex numbers is (4+33)+8i
Philip Williams

Philip Williams

Beginner2022-01-18Added 39 answers

Step 1
b) Convert to i into polar form as shown below.
Compare the complex number z=i with z=x+iy and obtain x=0 and y=1.
r=x2+y2
=0+1
=1
and,
θ=tan1(yx)
=tan1(10)
=π2
Step 2
Then the polar form of i is,
r(cosθ+isinθ)=1{cos(π2)+isin(π2)}
=1{cos(π22π)+isin(π22π)}
(Since cos(x2π)=cosx and sin(x2π)=sinx)
=1{cos(3π2)+isin(3π2)}
Therefore, the polar form of i is {{cos(3π2)+isin(3π2)}

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