Simplify in a +bi form?

Question

1. 3
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2- 3i

2. Express the sum of 4 + square -36 and -2 square -49 in a +b form.

I don't seem to undertstand the concept of the A + bi form forumla....

Answer 1

The easiest thing would be for you to look at the examples in your textbook.

The first one, look up "conjugate" in your book. You need to multiply the top and bottom by the conjugate of the denominator, or 2 + 3i.

You FOIL, and simplify. This is the process of rationalizing the denominator.

The second one, add (4 + 6i) + (-2 * 7i) I think. Your form in the question is difficult to understand.

(4 + 6i) + (-2 * 7i) = (4 + 6i) + (-14*i)

Answer 2

The a + bi form is the general way in which a number system is expressed. Here, i represents a number (not a "real" number) such that i squared equals -1. In common language, we say that i is the square root of -1.

When a and b can be any real number, then any "complex" number can be expressed in the form a + bi. Sometimes, when working in the complex field, you may get numbers that belong to the "real" line, such as +3. In such case, the complex part of the number (the "bi" portion) is zero.

There are other fields that can be written in the same form. For example, you can have an extended field that has all rational numbers (fractions made of integers only) and one irrational root (for example, square root of 2). In that case, any number can be written in the form a + b√2, where a and b are any rational number.

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Back to complex numbers... and your question

To resolve the second expression, you could transform each element in the form a + bi, then add together all the a's, then all the b's.

4 + √(-36) + -2√(-49) =

4 + √(-1)(36) - 2√(-1)(49) =

4 + 6√(-1) - 2(7)√(-1).

4 = 4 + 0i
6√(-1) = 0 + 6i
-14√(-1) = 0 - 14i

add all three together
a = 4 + 0 + 0 = 4
b = 0 + 6 - 14 = -8

Final answer in a + bi form:

4 - 8i

Answer 3

To simplify the first one you need to multiply both the numerator and the denominator by the complex conjugate of the denominator. In this case the complex conjugate is 2 + 3i

Numerator becomes: 3(2 + 3i) = 6 + 9i
Denominator becomes: (2 - 3i)(2+3i) = 4 + 6i - 6i - 9i^2 = 4 + 9 = 13

Answer= 6/13 + (9/13)i

the second one: 4 + 6i -2(7i) = 4 + 6i - 14i = 4 - 8i if I understood the question correctly.

Answer 4

If we assume "divided by technique of seven" applies to the entire expression, we are able to first divide the sq. root time period by technique of 40 9 (less than the sq. root signal) because 40 9 = 7^2 and then divide the different time period by technique of seven so as that the expression will develop into sqrt(-a million) - i^9. Now on account that sqrt(-a million) = i and any elementary skill of i = i, we in simple terms have i - i = 0, i.e. a = b = 0. i'm not confident if it really is what you want - however, assume that "divided by technique of seven" applies in effortless words to the in simple terms proper time period, so we get sqrt(-40 9) - i^9. because -40 9 = -a million x 40 9 we are able to rewrite sqrt(-40 9) as i x sqrt(40 9) = 7i. also i^9 = i as above, so the expression will develop into 6i, i.e. a = 0, b = 6. desire this facilitates.

Answer 5

a is the real # component and b is the imaginary component
3 = 3+0i
-3i = 0 -3i
4 +6i-2(7i)=4+6i-14i=4-8i