I some problems that I need help with please.
Add or subtact as indicated and write the results in standard form.
4. 6-(-5+7i)-(7-2i)
Divide and express the result in standard form. --These problems I don't understand, do you have to multply the denominator by the numerator?
7. (6-3i)/(9+2i)
8. (3-3i)/ (5-3i)
Perform the indicated operations and write the result in standard form.
17. (-4 - square root of -36)^2 I got -20+48i
19. ( square root of -16)(square root of -4) This one I don't understand.
25. (-42 + square root of -180)/6 this one I don't understand.
6-(-5+7i)-(7-2i) =
6 + 5 - 7i - 7 + 2i =
4 - 5 i
(6-3i)/(9+2i) =
(6-3i)(9-2i)/[(9+2i)(9-2i)]
(9-2i)(9+2i) = 81 + 4 = 85
(6-3i)(9-2i) = 54 -6 - 12i - 27i =
48 - 39 i
(-4 - square root of -36)^2 =
(-4 - 6 i)^2 =
(4+6i)^2 =
16 - 36 + 48 i = -20 + 48 i
( square root of -16)(square root of -4) =
4 i * 2i = -8
i= the square root of -1 if 3i (2+5i)= x+6i. Then x
3(square root of -1)(2+5(square root of -1)
-3(2+-5)
-9=x+6(square root of -1)
-9=x+-6
-9+-6=x
-15=x
To solve these problems, you need to know some rules and concepts related to complex numbers.
1. Addition and Subtraction of Complex Numbers:
To add or subtract complex numbers, you combine the real parts and the imaginary parts separately. For example:
6 - (-5 + 7i) - (7 - 2i) =
6 + 5 - 7i - 7 + 2i =
4 - 5i
2. Division of Complex Numbers:
To divide complex numbers, you need to simplify the expression by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number (a + bi) is (a - bi). For example:
(6 - 3i) / (9 + 2i) =
(6 - 3i) * (9 - 2i) / ((9 + 2i) * (9 - 2i)) =
(9 - 2i)(9 + 2i) = 81 + 4 = 85
(6 - 3i) * (9 - 2i) = 54 - 6 - 12i - 27i =
48 - 39i
So, the result is (48 - 39i) / 85.
3. Squaring and Square Roots of Complex Numbers:
To square a complex number, you multiply it by itself. For example:
(-4 - √(-36))^2 =
(-4 - 6i)^2 =
(4 + 6i)^2 =
16 - 36 + 48i =
-20 + 48i
To find the square root of a complex number, you take the square root of the real part and the imaginary part separately. For example:
√(-16) * √(-4) =
4i * 2i =
-8
4. Simplifying Complex Expressions:
To simplify an expression involving complex numbers, you follow the order of operations and apply the rules mentioned above. For example:
(-42 + √(-180)) / 6 =
(-42 + √(-36 * 5)) / 6 =
(-42 + 6i * 2√5) / 6 =
-7 + i√5
I hope this explanation helps you understand how to solve the given problems. If you have any more questions, feel free to ask.