Answer:
If you multiply a complex number by (1 + i) then the point on the complex plane will be scaled by √2 and rotated by an angle of 45°.
Explanation:
A polar number can be represented in polar form, wich is useful to see what happens when you multiply complex numbers.
Let z=x+iy represent a complex number. The representation of z in Polar Form is:
z = |z| (Cosα + iSinα)
Where |z| is the modulus of the complex number and α is the angle formed with the horizontal.
|z| = √x²+y²
α= arctan (y/x)
The complex numbers multiplication in the Polar Form is:
z1= |z1| (Cosα + iSinα)
z2= |z2|(Cosβ + iSinβ)
z1.z2 = |z1||z2| [Cos(α+β) + i Sin(α+β)]
Therefore, the magnitudes are multiplied and the angles are added (wich is rotating the complex number)
In this case, the given complex (Let c represent it) in the Polar Form is:
c = |c| (Cosβ + i Sinβ)
|c| = √1²+1² = √2
β = arctan(1/1) = 45°
If you multiply a complex number by (1 + i) then the point on the complex plane will be scaled by √2 and rotated by an angle of 45°.