Complex Numbers and Operations

The video tutorial explains how to handle complex numbers in fraction form, emphasizing that the imaginary unit 'i' should not appear in the denominator. It demonstrates how to simplify such fractions by multiplying by the conjugate, ensuring the denominator becomes a real number. The tutorial covers two examples: one with a purely imaginary denominator and another with both real and imaginary parts, showing step-by-step simplification using complex conjugates.

Why is it not allowed to have 'i' in the denominator when dividing complex numbers?

• Because it makes the expression undefined.

• Because it is similar to not having a square root in the denominator of a radical expression.

• Because 'i' is an imaginary number.

• Because 'i' is equal to the square root of -1.

What is the value of 'i' squared?

• 1

• -1

• i

• 0

What do we multiply by to eliminate 'i' from the denominator when it is an imaginary number?

• -1/i

• -i/-i

• i/i

• 1/i

What is the simplified form of -6i + 7i^2 / -3i^2?

• -7/3 - 2i

• -6i + 7

• -7/3 - 6/3i

• -7 - 6i

How can the quotient -7 - 6i be expressed in terms of real and imaginary parts?

• -7/3 - 2i

• -7 - 6i

• -7/3 - 6/3i

• -7/3 - 2/3i

What do we multiply by when the denominator has both a real and an imaginary part?

• The complex conjugate of the numerator

• The reciprocal of the numerator

• The complex conjugate of the denominator

• The reciprocal of the denominator

What is the complex conjugate of -3 + 4i?

• -3 - 4i

• -3 + 4i

• 3 + 4i

• 3 - 4i

What is the result of multiplying -2 by -3?

• -6

• -1

• 0

• 6

What is the simplified form of 26 - 7i / 25?

• 26 - 7/25i

• 26/25 - 7/25i

• 26 - 7i

• 26/25 + 7/25i

What is the value of 'i' squared used in the denominator?

• 1

• -1

• 0

• i