Question

Perform the indicated operations. Write the answer in standard form, a+bi.
(5 + 6i)(5 - 6i)

Answer 1

61

Explanation:

(5 + 6i)(5 - 6i)

FOIL

first: 5*5 =25

outer: 5 *-6i = -30i

inner: 6i *5 = 30i

last: 6i * -6i = -36 i^2 =-36 (-1) = 36

Add together

25 -30i+30i+36

61

Answer 2

`\boxed{\underline{\bf \: ANSWER}}`

`\sf \: ( 5 + 6 i ) ( 5 - 6 i )`

Multiply complex numbers 5+6i and 5-6i in the same way as you multiply binomials.

`\dashrightarrow \sf 5* 5+5* \left(-6i\right)+6i* 5+6\left(-6\right)i^(2)`

By definition, i² is -1.

`\dashrightarrow \sf 5* 5+5* \left(-6i\right)+6i* 5+6\left(-6\right)\left(-1\right)`

Do the multiplications.

`\dashrightarrow \sf \: 25-30i+30i+36`

Now cancel -30i & +30i

`\dashrightarrow \sf \: 25 \: \bcancel{- 30i} \: + \: \bcancel{30i}+36`

Now the equation becomes

`\dashrightarrow \sf \: 25 \: + 36 \\ \dashrightarrow \boxed{\bf \: 61}`

________

Hope it helps.

ŕάίήвόώşάĻţ2²2²