Question

If x+yi/i = 8+ 10i, where x and y are real, what is the value of (x + yi)(x - yi)?

A 164
B 150
C. 75
D. 100

Answer 1

A.164

Explanation:

(x+yi)(x-yi) -> (8+10i)(8-10i)

rule: *(a-b)(a+b)=a^2+b^2

(8+10i)(8-10i) = 64-100i^2

rule: i^2=(-1)

64-100i^2 = 64-100(-1)

=64+100

=164

Answer 2

164

Explanation:

(x + iy)/i = 8 + 10i

(x + iy) = (8 + 10i)(i) = 8i + 10i²

= -10 + 8i

(-10 + 8i)(-10 - 8i) = (-10)² + 8² = 164