Polar form complex numbers

Question

Perform operatins using the complex numbers below. Uses polar form and give all angles in radians in the interval  [0,2pi)

z1=1-i

z2=-i

a) z1z2=re^ie where r=________ and theta =_______

b) z1/z2=re^io where r=_______ and theta =_________

Answer 1

Step 1:

The complex numbers .

Write the complex number in polar form.

Substitute and in the polar form.

The argument is .

Hence, the polar form of complex numbers

Step 2:

(a)

Find .

Eulers formula: .

Substitute

Since,

(b)

Find .

Eulers formula: .

Substitute

Since,

Solution: