a) Given: z1=6∠30∘ and z2=4+5i What is the resultant of the given complex numbers? In...

William Boggs

William Boggs

Answered

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

Expert

2022-01-17Added 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

Expert

2022-01-18Added 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)}

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?