Question

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

Answer 1

Answer:

61

Step-by-step 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.

$\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)i^{2}$

By definition, i² is -1.

$\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)\left(-1\right)$

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.

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