Question

Given z1 = 1+i and z2 = 2+3i.

Answer 1

Answer:

(a) $w=2+5i-6=-4+5i$

Multiplicative inverse of w will be $\frac{1}{-4+5i}$

(B) As w is same as the product of $z_1\ and\ z_2$

So there multiplicative inverse will also be same

Step-by-step explanation:

We have given two complex numbers

$z_1=1+i$ and $z_2=3+2i$

(a) First we have to find $w=z_1z_2$

So $w=(1+i)(2+3i)=2+3i+2i+6i^2=2+5i+6i^2$

As we know that $i^2=-1$

So $w=2+5i-6=-4+5i$

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 $\frac{1}{-4+5i}$

Because when we multiply $-4+5i$ with $\frac{1}{-4+5i}$ it gives result as 1

(b) As w is same as the product of $z_1\ and\ z_2$

So there multiplicative inverse will also be same