Question

Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2
purely real number


non-real complex number

Answer 1

Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.

What are Purely real numbers and Non-real complex numbers?

Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.

The given expressions can be simplified in the following manner,

• $-i^2+i^3 = -(\sqrt{-1})^2+(\sqrt{-1} \times \sqrt{-1} \times \sqrt{-1}) = 1 -i$

• 7-5i

• $\sqrt{-6} = \sqrt{-1 \times 6} = \sqrt{-1} \times \sqrt{6} = 0+ i\sqrt{6}$

• i⁶ = (i²)³ = (-1)³ = -1 = -1 +0i

• 0+9i

• $(\sqrt{-5})^2 = (\sqrt{-1 \times 5})^2 = -1 \times 5 = -5+0i$

• -12 = -12+0i

• $2 -7i^2 = 2-7(-1) = 2+7 = 9+0i$

Purely real numbers (a+0i)

• -1 +0i
• -5+0i
• -12+0i
• 9+0i

Non-real complex number (0+bi)

• 1-i
• 7-5i
• 0+i√6
• 0+9i

Learn more about Purely real numbers and Non-real complex numbers:

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