Question

What is the multiplicative inverse of :
$(2 - 8i)(7 + 8i) \div 1 + i$
​

Answer 1

Step-by-step explanation:

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$\red{(2 - 8i)(7 + 8i) \div 1 + i}$

$\green{14 + 18i - 56i - 64i \div 1 + i}$

$\orange{ \frac{14 - 102i}{1 + i} }$

$\bold\blue{multiplicative \: inverse : }$

$\huge \boxed{\purple{ \frac{1 + i}{14 + 102i}}}$

Answer 2

Step-by-step explanation:

(2-8i) (7+8i)/1+i

Therefore,

Multiplicative Inverse

= 1+i/(2-8i) (7+8i)

= 1+i/14+16i-56i+64i^2

= 1+i/78-40i

= (1+i) (78+40i)/(78-40i) (78+40i)

= 78+40i+78i+40i^2/(78)^2-(40i)^2

= 38+118i/6084+1600

= 38+118i/7684