Powers of i (Level 1)

This math topic focuses on simplifying the powers of the imaginary unit \( i \). The problems involve calculating the result of \( i \) raised to various powers, such as \( i^7 \), \( i^2 \), \( i^3 \), \( i^0 \), \( i^1 \), \( i^4 \), and \( i^6 \). The worksheet provides multiple-choice answers for each question, helping to build understanding and familiarity with the cyclical nature of the powers of \( i \) in the complex number system. Each problem helps reinforce the fundamental cycles of \( i \) — where \( i^0 = 1 \), \( i^1 = i \), \( i^2 = -1 \), and \( i^3 = -i \), repeating every four exponents.

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

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Powers of i

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Simplify the power of i

i0i^{0}

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Complex Numbers - Powers of i Worksheet

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Math worksheet on 'Complex Numbers - Powers of i (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Simplify the power of i
A LaTex expression showing i to the power of 0
a A LaTex expression showing i
b A LaTex expression showing -i
c A LaTex expression showing -1
d A LaTex expression showing 1
2
Simplify the power of i
A LaTex expression showing i to the power of 4
a A LaTex expression showing -i
b A LaTex expression showing i
c A LaTex expression showing 1
d A LaTex expression showing -1
3
Simplify the power of i
A LaTex expression showing i to the power of 7
a A LaTex expression showing i
b A LaTex expression showing 1
c A LaTex expression showing -i
d A LaTex expression showing -1
4
Simplify the power of i
A LaTex expression showing i to the power of 2
a A LaTex expression showing i
b A LaTex expression showing 1
c A LaTex expression showing -1
d A LaTex expression showing -i
5
Simplify the power of i
A LaTex expression showing i to the power of 1
a A LaTex expression showing i
b A LaTex expression showing 1
c A LaTex expression showing -i
d A LaTex expression showing -1
6
Simplify the power of i
A LaTex expression showing i to the power of 6
a A LaTex expression showing 1
b A LaTex expression showing i
c A LaTex expression showing -i
d A LaTex expression showing -1
7
Simplify the power of i
A LaTex expression showing i to the power of 3
a A LaTex expression showing -i
b A LaTex expression showing -1
c A LaTex expression showing i
d A LaTex expression showing 1