Question

HELPPPP
Find the product of (x + (3+5i))2.

Answer 1

Identity used:-

`\boxed{\sf (a+b)^2=a^2+b^2+2ab}`

Now

`\\ \sf\longmapsto (x+(3+5i))^2`

`\\ \sf\longmapsto x^2+2x(3+5i)+(3+5i)^2`

`\\ \sf\longmapsto x^2+6x+10xi+3^2+2(3)(5i)+(5i)^2`

• i^2=-1

`\\ \sf\longmapsto x^2+6x+10xi+9+30i-25`

`\\ \sf\longmapsto x^2+6x+10xi+30i+9-25`

`\\ \sf\longmapsto x^2+6x+10xi+30i-16`

Answer 2

Use identities:

• (a + b)² = a² + 2ab + b²
• i² = -1

Simplify:

• (x + (3 + 5i))² =
• x² + 2x(3 + 5i) + (3 + 5i)² =
• x² + 6x + 10xi + 9 + 30i - 25 =
• x² + 6x + 10xi + 30i - 16