Grade 11 · Algebra & functions

Rewriting complex numbers practice

Rewriting complex numbers is a grade 11 math skill aligned to Common Core standard HSN.CN.A.2: use the relation i² = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 rewriting complex numbers problems our math games drill.

CCSS HSN.CN.A.210 questions in the bank
Sample questions

Try 8 for free

Question 1easy

Given i=1i = \sqrt{-1}, what is 49+4\sqrt{49} + \sqrt{-4}?

49=7\sqrt{49} = 7 and 4=2i\sqrt{-4} = 2i. So 49+4=7+2i\sqrt{49} + \sqrt{-4} = 7 + 2i.

Question 2easy

Given i=1i = \sqrt{-1}, what is 81+25\sqrt{81} + \sqrt{-25}?

81=9\sqrt{81} = 9 and 25=5i\sqrt{-25} = 5i. So 81+25=9+5i\sqrt{81} + \sqrt{-25} = 9 + 5i.

Question 3easy

Given i=1i = \sqrt{-1}, what is 4+16\sqrt{4} + \sqrt{-16}?

4=2\sqrt{4} = 2 and 16=4i\sqrt{-16} = 4i. So 4+16=2+4i\sqrt{4} + \sqrt{-16} = 2 + 4i.

Question 4easy

Given i=1i = \sqrt{-1}, what is 64+1\sqrt{64} + \sqrt{-1}?

64=8\sqrt{64} = 8 and 1=i\sqrt{-1} = i. So 64+1=8+i\sqrt{64} + \sqrt{-1} = 8 + i.

Question 5easy

Given i=1i = \sqrt{-1}, what is 100+49\sqrt{100} + \sqrt{-49}?

100=10\sqrt{100} = 10 and 49=7i\sqrt{-49} = 7i. So 100+49=10+7i\sqrt{100} + \sqrt{-49} = 10 + 7i.

Question 6medium

Given i=1i = \sqrt{-1}, what is 36+81\sqrt{36} + \sqrt{-81}?

36=6\sqrt{36} = 6 and 81=9i\sqrt{-81} = 9i. So 36+81=6+9i\sqrt{36} + \sqrt{-81} = 6 + 9i.

Question 7medium

Given i=1i = \sqrt{-1}, what is 4916\sqrt{49} - \sqrt{-16}?

49=7\sqrt{49} = 7 and 16=4i\sqrt{-16} = 4i. So 4916=74i\sqrt{49} - \sqrt{-16} = 7 - 4i.

Question 8medium

Given i=1i = \sqrt{-1}, what is 1219\sqrt{121} - \sqrt{-9}?

121=11\sqrt{121} = 11 and 9=3i\sqrt{-9} = 3i. So 1219=113i\sqrt{121} - \sqrt{-9} = 11 - 3i.

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