Rewriting Roots (Level 3)

This math topic focuses on advanced manipulation of complex numbers, specifically the skill of rewriting square roots that contain negative radicands into complex number expressions. Students are encouraged to simplify such expressions and manage radicals effectively, integrating both imaginary units and variable exponents. The problems involve interpreting and transforming complex algebraic structures that include powers and roots into their simplified complex forms. This is an advanced exercise aimed at deepening understanding of complex numbers and their properties in the context of algebra.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Complex Numbers - Rewriting Roots Worksheet

Mobius Math Academy logo
Math worksheet on 'Complex Numbers - Rewriting Roots (Level 3)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -80{p to the power of 2 }
a A LaTex expression showing 2pi
b A LaTex expression showing 2pisquare root of 4
c A LaTex expression showing 3pisquare root of 6
d A LaTex expression showing 3pi
e A LaTex expression showing 4pisquare root of 5
f A LaTex expression showing {p} to the power of 3 isquare root of 4
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{d to the power of 4 }
a A LaTex expression showing 2{d} to the power of 2 isquare root of 5
b A LaTex expression showing 3disquare root of 4
c A LaTex expression showing 5{d} to the power of 2 i
d A LaTex expression showing di
e A LaTex expression showing 3di
f A LaTex expression showing {d} to the power of 4 isquare root of 3
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -112{z to the power of 4 }
a A LaTex expression showing 5{z} to the power of 2 isquare root of 5
b A LaTex expression showing 3zisquare root of 6
c A LaTex expression showing 6zisquare root of 8
d A LaTex expression showing 6{z} to the power of 2 isquare root of 3
e A LaTex expression showing 5{z} to the power of 4 isquare root of 3
f A LaTex expression showing 4{z} to the power of 2 isquare root of 7
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -27{x to the power of 4 }
a A LaTex expression showing 3{x} to the power of 2 isquare root of 3
b A LaTex expression showing 5{x} to the power of 2 isquare root of 5
c A LaTex expression showing 5xi
d A LaTex expression showing {x} to the power of 3 i
e A LaTex expression showing 4xi
f A LaTex expression showing 3{x} to the power of 2 isquare root of 2
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -50{z to the power of 3 }
a A LaTex expression showing 8zisquare root of 2{z to the power of 2 }
b A LaTex expression showing 5{z} to the power of 3 isquare root of {z to the power of 3 }
c A LaTex expression showing 4{z} to the power of 3 isquare root of 4{z to the power of 3 }
d A LaTex expression showing 3{z} to the power of 3 isquare root of 4{z to the power of 3 }
e A LaTex expression showing 6{z} to the power of 3 isquare root of z
f A LaTex expression showing 5zisquare root of 2z
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -32z
a A LaTex expression showing 3isquare root of z
b A LaTex expression showing 6isquare root of z
c A LaTex expression showing 4isquare root of 2z
d A LaTex expression showing isquare root of 3z
e A LaTex expression showing isquare root of 2z
f A LaTex expression showing 7isquare root of 5z
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -112{x to the power of 4 }
a A LaTex expression showing 3{x} to the power of 3 isquare root of 4
b A LaTex expression showing 4{x} to the power of 4 isquare root of 4
c A LaTex expression showing 2xisquare root of 4
d A LaTex expression showing 4{x} to the power of 2 isquare root of 7
e A LaTex expression showing 2{x} to the power of 4 isquare root of 4
f A LaTex expression showing 2xisquare root of 6