Question

(5+2yi)(4-3i) - (5-2yi)(4-3i) in a + bi form, where y is a real number.

Answer 1

`(5+2yi)(4-3i) - (5-2yi)(4-3i)=\\(4-3i)(5+2yi-5+2yi)=\\(4-3i)\cdot4yi=\\16yi+12y=\\12y+16yi`

Answer 2

(5+2yi)(4-3i) - (5-2yi)(4-3i)

Factorize out (4 - 3i)

(4 -3i)( (5 + 2yi) - (5 -2yi) )

(4 -3i)(5 + 2yi - 5 + 2yi)

(4 -3i)(5 - 5 + 2yi + 2yi)

(4 -3i)4yi

4*4yi - 4yi*3i

= 16yi - 12yi². i² = -1

= 16yi - 12y(-1)

= 16yi + 12y

= 12y + 16yi in the form a + bi.