I need to write this functions in rectangular

Lisa Cooper

Lisa Cooper

Answered question

2022-04-07

I need to write this functions in rectangular coordinates:
f(r,θ)=r2k+5cos5θ
g(r,θ)=r2k+5cos5θ

Answer & Explanation

xcentricccrhb1

xcentricccrhb1

Beginner2022-04-08Added 12 answers

Write x+iy=reiθ, then (x+iy)5=r5e5iθ, so
r5cos5θ=Re(r5e5iθ)
=Re((x+iy)5)
=x5+10x3(iy)2+5x(iy)4
=x510x3y2+5xy4
and also
r5sin5θ=Im(r5e5iθ)
=5x410x2y3+y5
Now, use also that r2=x2+y2

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