Given z1 = 1+i and z2 = 2+3i.
a. let w = z1 ⋅ z2. find w and the multiplicative inverse of w.
b. show that the multiplicative inverse of w is the same as the product of the multiplicative inverses of z1 and z2.

(a)

Multiplicative inverse of w will be

(B) As w is same as the product of

So there multiplicative inverse will also be same

Step-by-step explanation:

We have given two complex numbers

and

(a) First we have to find

So

As we know that

So

Multiplicative inverse :

It is that number when multiply with the number which we have have to find the multiplicative inverse gives result as 1

So multiplicative inverse of w will be

Because when we multiply with it gives result as 1

(b) As w is same as the product of

So there multiplicative inverse will also be same

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step-by-step explanation: