Rewriting Roots (Level 4)

This math topic focuses on practicing complex numbers, specifically rewriting roots as complex numbers and simplifying radicals. Each problem presents a unique expression involving a square root of a negative product, which needs to be expressed in terms of complex numbers (using the imaginary unit \(i\)). It enhances understanding of the fundamental concepts of complex numbers and the manipulation of expressions involving powers and roots. The problems progressively build skills in simplifying and rewriting complex expressions in clearer forms and algebraic manipulation involving imaginary numbers.

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

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Complex Numbers - Rewriting Roots Worksheet

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Math worksheet on 'Complex Numbers - Rewriting Roots (Level 4)'. 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 -99{z to the power of 4 {r} to the power of 3 }
a A LaTex expression showing {z} to the power of 2 risquare root of 10{r to the power of 3 }
b A LaTex expression showing 3{z} to the power of 2 risquare root of 11r
c A LaTex expression showing zrisquare root of 14r
d A LaTex expression showing 6{z} to the power of 2 risquare root of 12r
e A LaTex expression showing 6{z} to the power of 4 risquare root of 10{r to the power of 3 }
f A LaTex expression showing 3zrisquare root of 8{r to the power of 2 }
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -48{d to the power of 3 r}
a A LaTex expression showing 5disquare root of 4dr
b A LaTex expression showing 4disquare root of 3dr
c A LaTex expression showing 5disquare root of dr
d A LaTex expression showing disquare root of dr
e A LaTex expression showing 5{d} to the power of 2 isquare root of {d to the power of 2 {r} to the power of 2 }
f A LaTex expression showing disquare root of 4{d to the power of 2 {r} to the power of 2 }
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -18y{m to the power of 3 }
a A LaTex expression showing 2{m} to the power of 2 isquare root of {y to the power of 2 m}
b A LaTex expression showing misquare root of ym
c A LaTex expression showing {m} to the power of 3 isquare root of 2{y to the power of 2 m}
d A LaTex expression showing 3misquare root of ym
e A LaTex expression showing 4misquare root of ym
f A LaTex expression showing 3misquare root of 2ym
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -48np
a A LaTex expression showing 7isquare root of 6n{p to the power of 2 }
b A LaTex expression showing 3isquare root of 2np
c A LaTex expression showing 4isquare root of 3np
d A LaTex expression showing 5isquare root of 4np
e A LaTex expression showing 7isquare root of np
f A LaTex expression showing 6isquare root of 3n{p to the power of 2 }
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63r{z to the power of 4 }
a A LaTex expression showing {z} to the power of 3 isquare root of 9r
b A LaTex expression showing zisquare root of 9r
c A LaTex expression showing 3{z} to the power of 2 isquare root of 7r
d A LaTex expression showing zisquare root of 5{r to the power of 2 }
e A LaTex expression showing 2{z} to the power of 3 isquare root of 9r
f A LaTex expression showing zisquare root of 4r
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -12{z to the power of 3 {r} to the power of 3 }
a A LaTex expression showing 2zrisquare root of 3zr
b A LaTex expression showing zrisquare root of 6zr
c A LaTex expression showing 5zrisquare root of 6zr
d A LaTex expression showing 2zrisquare root of 4{z to the power of 2 r}
e A LaTex expression showing 5{z} to the power of 2 risquare root of 6{z to the power of 2 r}
f A LaTex expression showing {z} to the power of 3 risquare root of {z to the power of 3 r}
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -12{n to the power of 4 {d} to the power of 3 }
a A LaTex expression showing ndisquare root of {d to the power of 2 }
b A LaTex expression showing 2{n} to the power of 2 disquare root of 3d
c A LaTex expression showing {n} to the power of 3 disquare root of {d to the power of 3 }
d A LaTex expression showing 2ndisquare root of 3d
e A LaTex expression showing 3{n} to the power of 3 disquare root of 3{d to the power of 2 }
f A LaTex expression showing {n} to the power of 4 disquare root of 4d