Math Djedji Polar Coordiantes with complex numbers

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Last updated 1:55 AM on 5/14/26
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11 Terms

1
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Rectangular form

a + bi

2
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Rectangular coordinates

(a,b)

3
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Polar form

r(cosθ+isinθ) or rcisθ

4
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Polar Coordinates

(r,θ)

5
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Complex Plane

argand plane

imaginary axis = y-axis

real axis = x-axis

6
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Modulus (r)

Absolute value of a complex number

r = √(a²+b²)

7
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Arguement (θ)

θ = tan-1(b/a)

8
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Multiply Complex Numbers

if

z1=r1(cosθ1+isinθ1)

z2=r2(cosθ2+isinθ2)

then

z1*z2=r1*r2(cos(θ1+θ2)+isin(θ1+θ2))

9
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Divide Complex Numbers

if

z1=r1(cosθ1+isinθ1)

z2=r2(cosθ2+isinθ2)

then

z1/z2=r1/r2(cos(θ1-θ2)+isin(θ1-θ2))

10
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De Moivre’s Theorem

if

z=r(cosθ+isinθ)

then

zn=rn(cosnθ+isinnθ)

11
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nth root of Z (complex number)

if

z=r(cosθ+isinθ)

then

z1/n=r1/n(cos((θ+2kpi)/n)+isin((θ+2kpi)/n))

where

k= 0,1,2,3, … n-1