The Basics
I am no longer in my cartesian form, I show my location via length and angle.
What is r ( Cosθ + iSinθ )
The argument of z1z2. PICTURE
65 degrees
When two cmplex numbers in polar form are multiplied, this is the mofulus.
What is r1 x r2?
This is the conjugate of A.
What is D?
The imaginary part of the complex number in Polar Form.
What is Sin𝛉?
This happens when I multiply two complex numbers.
What is the change in length and anticlockwise rotation.
The domain of the Argument of a complex number.
What is - π ≤ 𝛉 ≤ π ?
Finding the length of Z1Z2, this is to ne done.
What is adding √ 20 + √ 18 ?
Of these complex numbers this one had a modulus of 13. PICTURE
What is the modulus of -5 + 12i?
This is w2 in polar form. PICTURE
What is 16 [ cos(5 TT/6) + isin (5TT/6) ]?
If x is multiplied by i, it move like this around the argand plane.
What is 90o anticlockwise.
Using this complex number it gives direction in the 3rd quadrant.
-3 - i
What is -5TT / 6?
If Z1 = 1 + i, and Z2 = 2 - 3i , then this is equal to |Z1 / Z2|2
What is 2/13?
In converting to polar form this equals to x. PICTURE
What is 5 Cos 3 TT/ 4?
This argument always occur when z1 goes to the bottom. PICTURE
7 TT / 12
This is the definition of the argument.
The angle between the complex number and the real positive axis.
Since the complex number lies in the second quadrant, this would give its argument.
What is TT - tan-1 y/x ?
If Z = a + 3i, then this is a.
√2
Look at this diagram the arguement
What is
z = 2 + 2i expressed in polar form.
What is 2 [ Cos TT/4 + i Sin TT/4 ] ?
This gives the argument of two divided complex numbers
What is arg Z1 + arg Z2
This is the argument for my polar form. PICTURE
What is -1.97
θ = Sin-1 12 / 13 = 1.176
- TT + 1.176 =-1.97
This is my length if the area of a triangle is 50, formed by the complex numbers z , z + iz and iz.
10
On the Argand Diagram this is the position of the complex number in polar form. PICTURE
4th quadrant, 2 units long, θ = TT/6. PICTURE
If I do this to this polar equation it makes me revert to my cartesian ways. PICTURE
What is 2 Cos 2TT/3 + 2 Sin 2TT/3 i ?