Question

Which expression is equivalent to (4 +6i)^2??

-20 + 48i
8 + 12i
16 - 36i
20 + 48i

Answer 1

`-20+48 \text{i}`

Explanation:

Note that

`(4+6i)^2=4^2+2\cdot(4\cdot6i)+(6\cdot i)^2=16+48i+36i^2=16+48i-36\\\\=(36-13)+48i=-20+48i`

and we are done.

Answer 2

-20 + 48i

Explanation:

(4 +6i)^2 (Perfect square)

= (4)^2 + 2(4)(6i) + (6i)^2

= 16 + 48i + 36i^2

= 16 + 48i - 36 (i^2 = -1)

= -20 + 48i