Complex Numbers and Equations

This video tutorial on Positive Maths covers the equality of complex numbers, explaining that for two complex numbers to be equal, both their real and imaginary parts must be equal. The video provides three examples to illustrate how to solve equations involving complex numbers, including solving for variables and using simultaneous equations. The tutorial concludes with contact information for further inquiries.

What must be true for two complex numbers to be considered equal?

• Their imaginary parts must be equal.

• Their real parts must be equal.

• Both their real and imaginary parts must be equal.

• Their magnitudes must be equal.

In the equation x + i y + 6 - 9 i = 6 - 10 i, what is the value of x?

• 6

• 1

• 0

• -1

In the equation x + i y + 6 - 9 i = 6 - 10 i, what is the value of y?

• -1

• -9

• 0

• 1

What is the first step in solving the equation 2x - i y + y - x i = 1 - 5 i?

• Combine like terms.

• Add 5 to both sides.

• Equate the real parts and the imaginary parts separately.

• Multiply both sides by i.

In the equation 2x + y = 1 and -y - x = -5, what is the value of x?

• 1

• 4

• -4

• 0

In the equation 2x + y = 1 and -y - x = -5, what is the value of y?

• 9

• 0

• -9

• 5

What is the first step in solving the equation 2x - 1 + (x + y)i = y - 6 + (2y - 4)i?

• Multiply both sides by 2.

• Equate the real parts and the imaginary parts separately.

• Add 6 to both sides.

• Subtract 1 from both sides.

In the equation 2x - 1 = y - 6, what is the value of x when y = 3?

• -1

• 2

• 1

• 0

In the equation x + y = 2y - 4, what is the value of y when x = -1?

• 2

• 4

• 3

• 5

What is the purpose of multiplying the bottom line by -1 in the simultaneous equations?

• To simplify the equation.

• To eliminate y.

• To eliminate x.

• To make the coefficients equal.