Simplify 7 i − ( 3 − 25 i ) + − 81 7 i - ( 3 - 25 i ) + \sqrt { - 81 } 7 i − ( 3 − 25 i ) + − 81 and write in standard form.A) − 3 − 9 i - 3 - 9 i − 3 − 9 i B) − 3 + 41 i - 3 + 41 i − 3 + 41 i C) 29 i 29 i 29 i D) − 3 − 41 i - 3 - 41 i − 3 − 41 i E) 3 + 41 i 3 + 41 i 3 + 41 i

Question

Simplify   7 i − ( 3 − 25 i )  + − 81 7 i - ( 3 - 25 i )  + \sqrt { - 81 } 7 i − ( 3 − 25 i )  + − 81 ​   and write in standard form.A)    − 3 − 9 i - 3 - 9 i − 3 − 9 i B)    − 3 + 41 i - 3 + 41 i − 3 + 41 i C)    29 i 29 i 29 i D)    − 3 − 41 i - 3 - 41 i − 3 − 41 i E)    3 + 41 i 3 + 41 i 3 + 41 i

Ricardo Gonzalez · Accepted Answer

Final Answer : B, Explanation :   First, simplify the expression inside the parentheses and the square root. The square root of   − 81 -81 − 81   is   9 i 9i 9 i   (since   i = − 1 i = \sqrt{-1} i = − 1 ​  ). So, the expression becomes   7 i − 3 + 25 i + 9 i 7i - 3 + 25i + 9i 7 i − 3 + 25 i + 9 i  . Combining like terms, you get   − 3 + 41 i -3 + 41i − 3 + 41 i  , which is in standard form   a + b i a + bi a + bi  .

Simplify $\sqrt { - 81 }$ and write in standard form.

A) $- 3 - 9 i$
B) $- 3 + 41 i$
C) $29 i$
D) $- 3 - 41 i$
E) $3 + 41 i$

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Simplify 7i−(3−25i) +−817 i - ( 3 - 25 i ) + \sqrt { - 81 }7i−(3−25i) +−81​ and write in standard form.A) −3−9i- 3 - 9 i−3−9i B) −3+41i- 3 + 41 i−3+41i C) 29i29 i29i D) −3−41i- 3 - 41 i−3−41i E) 3+41i3 + 41 i3+41i

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Learning Objectives

Related questions

Simplify $\sqrt { - 81 }$ and write in standard form.

A) $- 3 - 9 i$
B) $- 3 + 41 i$
C) $29 i$
D) $- 3 - 41 i$
E) $3 + 41 i$