Show that x = 3 + 4/ is a solution to the equation x2 6x + 25 = 0. We will first substitute 3 + 4i for x in the left side of the equation. Then simplify powers of i and combine like terms to verify that it equals the right side of the equation. ])•: x² - 6x + 25 = 25 - (* - - 16/2) - 18 - 24i + 25 + 16 18 + 25) + (24i – 24i) + 6) =

Q: Express the following numbers in rectangular form (real and imaginary). (a) 9 39°= +i (b) 20 -15° =…

A: Note:as per our answering guidelines we can solve only 1 question or 3 sub parts. So i solved 1st…

Q: 1. Express the sum of (2 - 3i) and (6 + 4i) divided by the sum of (4 + i) and (-5- 2i) in a + bi…

A: 1)  To find the value of           {(2-3i)+(6+4i)} / {(4+i)+(-5-2i)}

Q: Divide (3 - 4i)/(4 + 3i) and express the result in standard form.

A: Multiply by the conjugate of the denominator

Q: Rewrite the complex number 3(cos 3.5 + i sin 3.5) in a + bi form a = b =

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Q: Write (3+2i)^4 in the simplified a+bi form

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Q: Multiply/Divide a) divide -27 • divide -27 b) (1+5i) (1- 5i)

A:

Q: Find all solutions of the following equationsa a)z/1-z=1-5i   b) (2-i)z+8z^2=0.  c)z^4-16=0

A: a). z1-z = 1 - 5i⇒ z = (1-5i)(1-z)⇒ z = 1 - z - 5i + 5iz⇒ (2 - 5i)z = 1-5i⇒ z = 1-5i2-5i

Q: Determine the product of (1 + i) and (1–31) A) 4- 2i B) 2 + 4i c) 2- 2i D) 2-4i

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Q: 4. Perform the indicated operation and express the answer in simplest a+bi form: a) (-25+…

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Q: Simplify (4 + 2i) +(-3- 5i) Answers must be in simplified radical form. No decimal approxin given…

A: Let y=(4+2i)+(-3-5i)

Q: (3 + 7i) 2 – 3i)

A: Follow next step

Q: |Write the following numbers in a + bi form: -2 – 5i (a) -1+ 2i + i, -1 -5 + 3i (b) i, 5i (c) (–5i)³…

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Q: Simplify the expression to a + bi form: (1+ 7i) + (4 – 10i) -

A: The given expression is 1+7i+4-10i.

Q: 2 The roots of the equation X + 2x+ 5 0 a 1) -3 and 1 2) -1, only 3)-1+ 2i and 1- 2i 4) -1+4i and…

A: given equation :

Q: When 3+4i / 2+i is expressed in the form a + bi, what is the value of a?

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Q: The United States' national debt is estimated at1.4 × 10² dollars. A very wealthy American has…

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Q: Calculate (-(2/3) + 2/3i)-4 Give your answer in the form a + bi, where a and b are exact real…

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Q: True or False The conjugate of 2 + 5i is - 2 - 5i.

A: The conjugate of 2+5i is -2-5i. The given statement is false.

Q: Solve for x (round to the nearest degree) 4 7

A: