Question

Which complex number from the table multiplied with B from the table will result in the product 159 + 27i?

A -3 − 4i
B -7 − 6i
C 13 + i
D -9 + 6i
E 8 − 8i
F -15 + 9i
G 2 + 12i
H 6 − 10i

Answer 1

Multiplying F with B results in the complex expression 159 + 27i:

(B)(F)

=

(-7 − 6i)(-15 + 9i)

=

105 − 63i + 90i − 54i2 (Apply the FOIL method.)

=

105 + 27i − 54(-1) (i2 = -1)

=

105 + 27i + 54

= 159 + 27i

Explanation:

Plato answer

Answer 2

F. -15 + 9i

Explanation:

B = (-7 -6i)

Multiply B by F = (-15 + 9i), would give;

B × F = (-7 -6i) × (-15 + 9i)

= -7 (-15 + 9i) - 6i (-15 + 9i)

= 105 -63i + 90i - 54(
`i^(2)`)

But
`i^(2)` = -1, so that:

105 -63i + 90i -54(
`i^(2)`) = 105 -63i + 90i -54(-1)

= = 105 -63i + 90i + 54

= 159 + 27i

B × F = 159 + 27i

Thus the required complex number is F (-15 + 9i).