Explain the geometric representation of multiplying a complex number by 1 + i.

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°.

Step-by-step 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°.

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.