1.3 Hw Q's Math

The imaginary unit i^2 is defined as i^2 =

-1

Multiply. √-3 x √-3 =

-3

Perform the indicated operations. (4 - 6 i)(9 + i)

42 - 50 i

Write the number as the product of a real number and i: √-112 =

4√7 i

Subtract and simplify. (4 + 3i) - (-1 - i)

5 + 4 i

Divide. 9 + 8i / 1 + 6i

57/37 - 46i/37

Write the number as the product of a real number and i: √-36 =

6i

Find the quotient. Write the answer in standard form a + bi. -8/i

8i

The numbers 6 + 5i and 6 - 5i, which differ only in the sign of their imaginary parts are

complex conjugates

If a and b are real​ numbers, then any number of the form a + bi is a(n)

complex number

Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.) 9

complex, real

Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.) 𝝅

complex, real

To find the quotient of two complex numbers in standard​ form, multiply both the numerator and the denominator by the complex conjugate of the

denominator

Decide whether the given statement is true or false. If​ false, correct the right side of the equation. ( -5 + 7i) - (-10 - 6i) = - 15 + i

false, - 15 + 13 i

Decide whether the given statement is true or false. If​ false, correct the right side of the equation. (9 + 5 i)^2 = 56

false, 56 + 90 i

Simplify. i^33

i

Add and simplify. (4 + 3i)(5 - 2i)

i + 9

Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.) 2 + 4 i

nonreal complex, complex

Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.) √-4

nonreal complex, complex, pure imaginary

Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions will​ apply.) 9i

nonreal complex, pure imaginary, complex

The product of a complex number and its conjugate is always​ a(n)

real number

Decide whether the given statement is true or false. If​ false, correct the right side of the equation. t^12 = 1

true

Decide whether the given statement is true or false. If​ false, correct the right side of the equation. √-144 = 12i

true

Decide whether the given statement is true or false. If​ false, correct the right side of the equation. √-9 x √-25 = - 15

true

The imaginary unit i is defined as i =

√-1

Divide. √-567/√-81 =

√7