Multiply ( 3 + 8 i ) ( 2 − 13 i ) ( 3 + 8 i ) ( 2 - 13 i ) ( 3 + 8 i ) ( 2 − 13 i ) and write in standard form.A) − 110 + 23 i - 110 + 23 i − 110 + 23 i B) 23 + 110 i 23 + 110 i 23 + 110 i C) − 110 − 23 i - 110 - 23 i − 110 − 23 i D) 110 − 23 i 110 - 23 i 110 − 23 i E) − 23 − 23 i - 23 - 23 i − 23 − 23 i

Question

Multiply   ( 3 + 8 i )  ( 2 − 13 i )  ( 3 + 8 i )  ( 2 - 13 i )  ( 3 + 8 i )  ( 2 − 13 i )    and write in standard form.A)    − 110 + 23 i - 110 + 23 i − 110 + 23 i B)    23 + 110 i 23 + 110 i 23 + 110 i C)    − 110 − 23 i - 110 - 23 i − 110 − 23 i D)    110 − 23 i 110 - 23 i 110 − 23 i E)    − 23 − 23 i - 23 - 23 i − 23 − 23 i

Simeon Skoufezis · Accepted Answer

Final Answer : D, Explanation :   Apply the distributive property and use the fact that $i^2=-1$. ( 3 + 8 i ) ( 2 − 13 i ) = 3 ( 2 ) − 3 ( 13 i ) + 8 i ( 2 ) − 8 i ( 13 i ) = 6 − 39 i + 16 i + 104 = 110 − 23 i  ( 3 + 8 i ) ( 2 - 13 i )  & = 3(2) - 3(13i) + 8i(2) - 8i(13i)\ & = 6 - 39i + 16i + 104\ & =110 - 23i  ( 3 + 8 i ) ( 2 − 13 i ) ​ = 3 ( 2 ) − 3 ( 13 i ) + 8 i ( 2 ) − 8 i ( 13 i ) = 6 − 39 i + 16 i + 104 = 110 − 23 i ​ Therefore, the answer is choice D.

Multiply $(3 + 8 i) (2 - 13 i)$ and write in standard form.

A) $- 110 + 23 i$
B) $23 + 110 i$
C) $- 110 - 23 i$
D) $110 - 23 i$
E) $- 23 - 23 i$

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Learning Objectives

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Multiply (3+8i) (2−13i) ( 3 + 8 i ) ( 2 - 13 i ) (3+8i) (2−13i) and write in standard form.A) −110+23i- 110 + 23 i−110+23i B) 23+110i23 + 110 i23+110i C) −110−23i- 110 - 23 i−110−23i D) 110−23i110 - 23 i110−23i E) −23−23i- 23 - 23 i−23−23i

Definitions

Learning Objectives

Learning Objectives

Related questions

Multiply $(3 + 8 i) (2 - 13 i)$ and write in standard form.

A) $- 110 + 23 i$
B) $23 + 110 i$
C) $- 110 - 23 i$
D) $110 - 23 i$
E) $- 23 - 23 i$