complex number problems with solutions - If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

Given,, \frac{x+yi}{i} = 7+9i

x+ yi = (7 + 9i) i

x + yi = 7i+ 9i^{2} (using distributive property of multiplication)

x+ yi = 7i - 9 (since i^{2} = -1)

This can be written as x+yi = -9 + 7i

x - yi = -9 -7i

So (x+yi)(x-yi) = (-9 + 7i)(-9 -7i) = 81 + 63 i -63 i -7^{2}i^{2} = 81+49 = 130

Skills to recall:

What is the distributive property of multiplication