Complex numbers Questions and Answers
![Simplify the expression to a + bi form:
√100+√-27-√√4+ √−108](https://media.kunduz.com/media/sug-question/raw/59244264-1657876852.826837.jpeg?w=256)
![Simplify the expression to a + bi form:
√9-√-2+√64+ √-18](https://media.kunduz.com/media/sug-question/raw/59242598-1657876754.6321795.jpeg?w=256)
![Express in simplest a + bi form:
(6-5yi) (5-i) + (6 - 5yi)(2+i)](https://media.kunduz.com/media/sug-question/raw/59241959-1657876568.8244696.jpeg?w=256)
![If a = -3 and b = -i, then find the value of a³b in fully simplified form.
Answer:
Submit Answer](https://media.kunduz.com/media/sug-question/raw/59242318-1657876443.7880325.jpeg?w=256)
Math
Complex numbersIf a = -3 and b = -i, then find the value of a³b in fully simplified form.
Answer:
Submit Answer
![Express (2/3 + √2/3i)² in simplest a + bi form.](https://media.kunduz.com/media/sug-question/raw/59242238-1657876394.4984593.jpeg?w=256)
![(4-3i) ² in simplest a + bi form.
Express √5
Answer:
Submit Answer](https://media.kunduz.com/media/sug-question/raw/59242304-1657876384.0348475.jpeg?w=256)
![Write as a trinomial in simplest form:
(4z -3i)²](https://media.kunduz.com/media/sug-question/raw/59240585-1657876235.527225.jpeg?w=256)
![Write as a trinomial in simplest form:
(4y - 51)2](https://media.kunduz.com/media/sug-question/raw/59240254-1657876099.116036.jpeg?w=256)
![Simplify the expression to a + bi form:
(-7-9i) + (10 + 10i)](https://media.kunduz.com/media/sug-question/raw/59246176-1657876001.9308035.jpeg?w=256)
![Simplify the expression to a + bi form:
-√81-√-20+√1+√-80](https://media.kunduz.com/media/sug-question/raw/59242222-1657875939.6822295.jpeg?w=256)
![Watch help video
If a = -5i and b = 2 + i, then find the value of a³b in fully simplified form.
Answer:
Submit Answer](https://media.kunduz.com/media/sug-question/raw/59244530-1657875853.3409836.jpeg?w=256)
Math
Complex numbersWatch help video
If a = -5i and b = 2 + i, then find the value of a³b in fully simplified form.
Answer:
Submit Answer
![Simplify the expression to a + bi form:
(4+2i)+(-12-2i)](https://media.kunduz.com/media/sug-question/raw/59246045-1657875820.8064082.jpeg?w=256)
![Write √-18 in simplest radical form.](https://media.kunduz.com/media/sug-question/raw/59242297-1657865524.2128499.jpeg?w=256)
![Simplify the expression to a + bi form:
(-7-3i)(11- 8i)](https://media.kunduz.com/media/sug-question/raw/59240563-1657834117.1263168.jpeg?w=256)
![Simplify the expression to a + bi form:
(11 +5i)(-10-8i)](https://media.kunduz.com/media/sug-question/raw/59240288-1657834081.0322948.jpeg?w=256)
![A fossilized leaf contains 34% of its normal amount of carbon 14. How old is the fossil to the nearest year? Use 5600 years as the half-life of carbon 14.
A. 33,849
B. 3,357
C. 28,490
D. 8,716](https://media.kunduz.com/media/sug-question/raw/59035856-1657819724.7325628.jpeg?w=256)
Math
Complex numbersA fossilized leaf contains 34% of its normal amount of carbon 14. How old is the fossil to the nearest year? Use 5600 years as the half-life of carbon 14.
A. 33,849
B. 3,357
C. 28,490
D. 8,716
![Information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 6; zeros: 2, 4+7i, -7-3i, 0](https://media.kunduz.com/media/sug-question/raw/58820427-1657751891.180556.jpeg?w=256)
Math
Complex numbersInformation is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 6; zeros: 2, 4+7i, -7-3i, 0
![Multiply. (-5+3i)(-6+2i) Write your answer as a complex number in standard form.](https://media.kunduz.com/media/sug-question/raw/58595912-1657733970.9235668.jpeg?w=256)
![Express √-64-√-49 as a complex number in standard form:
√64-√√ 49 =
Question Heln:](https://media.kunduz.com/media/sug-question/raw/57860739-1657680966.5211556.jpeg?w=256)
Math
Complex numbersExpress √-64-√-49 as a complex number in standard form:
√64-√√ 49 =
Question Heln:
![Consider the following polynomial inequality.
x²(x + 8)(x - 1) > 0
Step 1 of 2: Set one side equal to zero and list the interval endpoints (the only points at which the non-zero expression can change sign).](https://media.kunduz.com/media/sug-question/raw/57008343-1657563169.509029.jpeg?w=256)
Math
Complex numbersConsider the following polynomial inequality.
x²(x + 8)(x - 1) > 0
Step 1 of 2: Set one side equal to zero and list the interval endpoints (the only points at which the non-zero expression can change sign).
![What is the value of the modulus of 6 - 4i?
Enter your answer as a simplified radical in the box.](https://media.kunduz.com/media/sug-question/raw/76255867-1657524179.873711.jpeg?w=256)
Math
Complex numbersWhat is the value of the modulus of 6 - 4i?
Enter your answer as a simplified radical in the box.
![If v= 2i - 3j and w=xi + 9j, find all numbers x for which ||v+w|| = 7.
Select the correct choice and fill in any answer boxes in your choice below.
A. x =
B. There is no solution.](https://media.kunduz.com/media/sug-question/raw/74450964-1657485539.5566967.jpeg?w=256)
Math
Complex numbersIf v= 2i - 3j and w=xi + 9j, find all numbers x for which ||v+w|| = 7.
Select the correct choice and fill in any answer boxes in your choice below.
A. x =
B. There is no solution.
![Rewrite the expression in a + bi form: -3 + i/6 +6i](https://media.kunduz.com/media/sug-question/raw/62316576-1657398724.7900484.jpeg?w=256)
![Use a calculator to perform the indicated operations. Give the answer in rectangular form,
expressing real and imaginary parts to four decimal places.
55(cos7π/9 + i sin7π/9)/27.5 (cos3π/8+ i sin3π/8)](https://media.kunduz.com/media/sug-question/raw/62025850-1657396586.6713386.jpeg?w=256)
Math
Complex numbersUse a calculator to perform the indicated operations. Give the answer in rectangular form,
expressing real and imaginary parts to four decimal places.
55(cos7π/9 + i sin7π/9)/27.5 (cos3π/8+ i sin3π/8)
![Let z = -5 + 6i, and 22 = a + bi. What are the values of a and b?
a =
and
b=](https://media.kunduz.com/media/sug-question/raw/61756008-1657387915.759654.jpeg?w=256)
![Determine the polar form of the complex number 5-3i. Express the angle in degrees, where 0 ≤ θ ≤ 360°, and round numerical entries in the answer to two decimal places.
5.83(cos329.04° - isin329.04°)
329.04(cos329.04°-isin329.04°)
329.04(cos5.83 + isin5.83°)
5.83(cos329.04° + isin329.04°)](https://media.kunduz.com/media/sug-question/raw/61270990-1657321619.3737264.jpeg?w=256)
Math
Complex numbersDetermine the polar form of the complex number 5-3i. Express the angle in degrees, where 0 ≤ θ ≤ 360°, and round numerical entries in the answer to two decimal places.
5.83(cos329.04° - isin329.04°)
329.04(cos329.04°-isin329.04°)
329.04(cos5.83 + isin5.83°)
5.83(cos329.04° + isin329.04°)
![Add or subtract. Write the answer in standard form.
(17-12i) - (17 – 6i)
Oa - 18i
Ob 34 - 18i
Oc 34 - 6i
Od -6i](https://media.kunduz.com/media/sug-question/raw/60780076-1657289134.568464.jpeg?w=256)
Math
Complex numbersAdd or subtract. Write the answer in standard form.
(17-12i) - (17 – 6i)
Oa - 18i
Ob 34 - 18i
Oc 34 - 6i
Od -6i
![Write z₁ and 22 in polar form. (Express in radians. Let 0 ≤ θ < 2x.)
z₁ = √2-√2i , z2 = 1 - i
z1=
z2 =
Find the product z₁z2 and the quotients z1/z2 and 1/z1. (Express your answers in polar form with expressed in radians.)
z1z2=
z1/z2=
1/z1=](https://media.kunduz.com/media/sug-question/raw/60705877-1657280910.6690338.jpeg?w=256)
Math
Complex numbersWrite z₁ and 22 in polar form. (Express in radians. Let 0 ≤ θ < 2x.)
z₁ = √2-√2i , z2 = 1 - i
z1=
z2 =
Find the product z₁z2 and the quotients z1/z2 and 1/z1. (Express your answers in polar form with expressed in radians.)
z1z2=
z1/z2=
1/z1=
![Given that 3-4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x) = x² - 16x³ + 109x²-394x + 600](https://media.kunduz.com/media/sug-question/raw/60617078-1657276176.0697036.jpeg?w=256)
Math
Complex numbersGiven that 3-4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x) = x² - 16x³ + 109x²-394x + 600
![Solve the equation using factoring or the quadratic formula, whichever is appropriate.
a³ - 64 = 0
The real solution for a is 4 where the imaginary solutions are
1 +4 + 4 / 1
Hint: Your input was 4 and(1+-4i4)/1](https://media.kunduz.com/media/sug-question/raw/60410785-1657219672.5347178.jpeg?w=256)
Math
Complex numbersSolve the equation using factoring or the quadratic formula, whichever is appropriate.
a³ - 64 = 0
The real solution for a is 4 where the imaginary solutions are
1 +4 + 4 / 1
Hint: Your input was 4 and(1+-4i4)/1
![Find the quotient 5i / (1 - i) and express it in rectangular form by first converting the numerator and the denominator to trigonometric form.
(Type your answer in the form a+bi. Use integers or fractions for any numbers in the expression)](https://media.kunduz.com/media/sug-question/raw/60341713-1657219359.0825374.jpeg?w=256)
Math
Complex numbersFind the quotient 5i / (1 - i) and express it in rectangular form by first converting the numerator and the denominator to trigonometric form.
(Type your answer in the form a+bi. Use integers or fractions for any numbers in the expression)
![Which of the following represents vector t = -5i + 12j in trigonometric form?
a)t= 13 (cos 67.38°, sin 67.38°)
b)t= 13 (sin 67.38°, cos 67.38°)
c)t= 13 (cos 112.62°, sin 112.62°)
d)t= 13 (sin 112.62°, cos 112.62%)](https://media.kunduz.com/media/sug-question/raw/63725519-1656941199.2738965.jpeg?w=256)
Math
Complex numbersWhich of the following represents vector t = -5i + 12j in trigonometric form?
a)t= 13 (cos 67.38°, sin 67.38°)
b)t= 13 (sin 67.38°, cos 67.38°)
c)t= 13 (cos 112.62°, sin 112.62°)
d)t= 13 (sin 112.62°, cos 112.62%)