%5E2.jpeg "(-3i)^2")
Simplifying (-3i)^2
In mathematics, the expression (-3i)^2 can be simplified using the rules of complex numbers.
Understanding Complex Numbers
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as √-1.
Simplifying (-3i)^2
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Expand the expression: (-3i)^2 = (-3i) * (-3i)
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Apply the distributive property: (-3i) * (-3i) = 9i^2
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Substitute i^2 with -1: 9i^2 = 9(-1)
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Simplify: 9(-1) = -9
Therefore, (-3i)^2 = -9.
Key Points
- The square of an imaginary number is always a real number.
- Remember that i^2 = -1.
- When simplifying complex numbers, follow the rules of arithmetic and algebra.