Polar to Rectangular form of complex number Example-1

1. `r=3, theta=pi/6` rad
Find Rectangular form of complex number

Solution:

For polar coordinates `(r,theta)`, the rectangular form is `z=a+bi`
where `a=r*cos(theta)` and `b=r*sin(theta)`

`r=3, theta=pi/6` rad

`a=3*cos(pi/6)=3*0.866=2.5981`

and `b=3*sin(pi/6)=3*0.5=1.5`

`:.` rectangular form is `z=a+bi=2.5981+1.5i`

2. `r=2, theta=pi/3` rad
Find Rectangular form of complex number

Solution:

For polar coordinates `(r,theta)`, the rectangular form is `z=a+bi`
where `a=r*cos(theta)` and `b=r*sin(theta)`

`r=2, theta=pi/3` rad

`a=2*cos(pi/3)=2*0.5=1`

and `b=2*sin(pi/3)=2*0.866=1.7321`

`:.` rectangular form is `z=a+bi=1+1.7321i`

3. `r=3, theta=30` deg
Find Rectangular form of complex number

Solution:

For polar coordinates `(r,theta)`, the rectangular form is `z=a+bi`
where `a=r*cos(theta)` and `b=r*sin(theta)`

`r=3, theta=30` deg

`a=3*cos(30)=3*0.866=2.5981`

and `b=3*sin(30)=3*0.5=1.5`

`:.` rectangular form is `z=a+bi=2.5981+1.5i`

4. `r=2, theta=60` deg
Find Rectangular form of complex number

Solution:

For polar coordinates `(r,theta)`, the rectangular form is `z=a+bi`
where `a=r*cos(theta)` and `b=r*sin(theta)`

`r=2, theta=60` deg

`a=2*cos(60)=2*0.5=1`

and `b=2*sin(60)=2*0.866=1.7321`

`:.` rectangular form is `z=a+bi=1+1.7321i`

This material is intended as a summary. Use your textbook for detail explanation.
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