Question

1. Suppose c = -11 + 3i. What two nonzero complex numbers could have been

added together to make c?
2. Find the value of iº.

Answer 1

There are many pairs of complex numbers that can sum to c = -11 + 3i, such as (-8 + 2i) and (-3 + i). Also, i^0 is equal to 1, as is the case with any non-zero number raised to the power of zero.

Step-by-step explanation:

There are infinitely many pairs of nonzero complex numbers that can be added together to obtain c = -11 + 3i. Two examples could be (-8 + 2i) and (-3 + i), or (-10 + 4i) and (-1 - i). Adding these pairs will result in the given complex number:

• (-8 + 2i) + (-3 + i) = -11 + 3i
• (-10 + 4i) + (-1 - i) = -11 + 3i

The value of i^0, by the definition of any non-zero number raised to the power of zero, is 1.

Answer 2

Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:

a + b = -11

ai + bi = 3i

Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:

ai + bi = 3i

-ai - bi = 11i

0 + 10bi = 14i

Simplifying, we get b = 1.4. Substituting this into the first equation gives:

a + 1.4 = -11

a = -12.4

So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.

To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:

e^(iθ) = cos(θ) + i sin(θ)

So we have:

iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Therefore, iº = i.

Step-by-step explanation: