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°.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared