Question

Given that X=3+8i and y=7−1i, match the equivalent expression:

a) X+y
b) X−y
c) X×y
d) X/y

Answer 1

To find the equivalent expression, we need to perform the given operations between X and y. The equivalent expressions are: a) X+y = 10 + 7i, b) X-y = -4 + 9i, c) X×y = 21 + 45i, d) X/y = 23/50 + (59/50)i.

Step-by-step explanation:

To find the equivalent expression, we need to perform the given operations between X and y. Let's go through the options:

a) X+y: (3+8i) + (7-1i) = 10 + 7i

b) X-y: (3+8i) - (7-1i) = -4 + 9i

c) X×y: (3+8i) * (7-1i) = (3*7 - 8i*1) + (3*-1i + 8i*7) = 21 - 8i + (-3i + 56i) = 21 + 45i

d) X/y: (3+8i) / (7-1i) = ((3+8i)*(7+1i))/(7^2 - (-1i)^2) = (23 + 59i)/50 = 23/50 + (59/50)i

So, the equivalent expressions are: a) X+y = 10 + 7i, b) X-y = -4 + 9i, c) X×y = 21 + 45i, d) X/y = 23/50 + (59/50)i.