Imaginary numbers

If z = a - bi, which of the following must be true of the imaginary part of the complex conjugate of z?

It must be the opposite of -b.

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?

The imaginary part is zero.

Multiply the following complex numbers. Reduce terms and simplify. Explain how your simplified result and the first term in the pair below are related algebraically to each other and to the complex number (1 + i).

1/2 - i/2

Find the sum of 3 - 7i and 8 + 4i.

11 - 3i

i 12 + 1 =

2

(5 - i)(5 + i) =

26

(3 - i) + (1 - 2i) =

4 - 3i

(7 + 3i) - (2 + 3i) =

5

Perform the indicated multiplication below. Reduce terms and simplify. Include all of the necessary steps and calculations in your final answer. (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)

50+50i

(half correct) Match each description when z = 9 + 3i. 1. Real part of z 3i 2. Imaginary part of z 9 - 3i 3. Complex conjugate of z 9 4. 3i - z 3 5. z - 9 -9 6. 9 - z -3i

6, 3, 1, 2, 5, 4

10(4 - 3i) =

40 - 30i

i 15 =

-i

Find the multiplicative inverse of 6 + 2i.

1/(6 + 2i)

i 6 =

-1

Find the complex conjugate of 0.5 - 0.25i.

0.5 + 0.25i

Simplify each expression using the definition, identities, and properties of imaginary numbers. Match each term in the list on the left to its equivalent simplified form on the right. 1. (i 3)2(-i 0)3(3i 2)4 -4 2. (i 3i -5)2(i 4i -3)0 1 3. (-i 4i 2)(2i)2(i -1i 5)3(i 0)-3 81 4. i 3[(i 2i 3i 4)(i 0i 2i 5)]2 -i

3, 2, 1, 4

Use the definition, identities, and properties of imaginary numbers to simplify each of the following expressions. Match each item with its correct simplest form. 1. (i 3)5 i 2. -i 6 · i 3 · i -5 -1 3. -(i 4) (i 0) (i 7) -i 4. (i 5 · i -2 · i 8)0 1

3, 2, 1, 4

(-3 - 5i)(-3 + 5i) =

34