Write in the form x+yi: 2+3i (a) 1+i -4+3i (b) -2 -i 4i (c) 2-i 1 (d) 2+3i 3- 2i (e) i p+qi (f) r+si

Q: Write each of the following in standard form.(a) (1 + 4i ) / (5 - 12i )(b) ( 2 - 3i ) / (4 - 3i)

A: a) Given that,  1+4i5-12i Simplification: 1+4i5-12i=1+4i5-12i×5+12i5+12i                Rationalize…

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

A: Multiply by the conjugate of the denominator

Q: PWrite the following numbers in a + bi form: -1- 3i (a) 5 – i + i, | 4 -5 + (b) + i, 2i 4i (c)…

A: a Given expression is −1−3i5−i. We have to write the given expression in a+bi form. Rationalize the…

Q: Simplify the expression -i+ (7+ 8i) 2i(-6+2i) + - 1-i to the form a + y · i where a and y are real…

A: The given expression 2i-6+2i+-i+7+8i¯¯1-i. Simplify the expression 2i-6+2i+-i+7+8i¯¯1-i in standard…

Q: Write 1/ (3 + 4i ) in standard form a + bi; that is, find the reciprocal of 3 + 4i.

A:

Q: (2+3i)(5-i) Simplify (3-2i)2

A:

Q: Simplify the expression to a + bi form: (-6 – 9i)(-11 +7i)

A:

Q: Simplify the expression to a + bi form: (-8 — 2:) + (8 — і)

A: (- 8 - 2i) + (8 - i) = (- 8 + 8) + (- 2i - i) = 0 + (- 3)i  So, a = 0 &, b = - 3

Q: (-4+i)-(5-7i)² Simplify 3i

A: We use i2=-1

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

A:

Q: Divide and express the result in standard form: 5i /(2 - i)

A: The given expression is 5i2-i

Q: 31) Simplify and express with positive exponents: -8y3

A:

Q: Divide and express the result in standard form: (7 + 4i) / (2 - 5i).

A: 7+4i2-5i

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: Simplify the expression to a + bi form: (5 + 2i)(8 + 8i)

A: (5+2i)(8+8i) = 24 + 56i  The detailed solution is as follows below

Q: (5i)-(2i)-(8+4i) simplify

A: (5i)-(2i)-(8+4i) simplify

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

A:

Q: Write the following numbers in a + bi form: -1 - 4i + i, -2 – 3i 1 -3 + i, 3i 4i =) (i)³ + i. +

A: Topic:- complex number algebra

Q: Simplify and express in standard form: 1-5i/1+5i

A:

Q: Perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i) - (3 -…

A: Given 2-3i1-i-3-i3+i

Q: (7i)(7i)(5-6i)

A:

Q: Divide and express the result in standard form: (5 + 4i) / (4 - i).

A: Given:5+4i4-i

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

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

Q: Divide and express the result in standard form: (2 + 3i)/(2 + i)

A: The given expression is (2 + 3i)/(2 + i)

Q: Divide and express the result in standard form: 2i/(1 + i)

A:

Q: Simplify the expression to a + bi form: (-9 – 8i) – (–4+ 5i)

A: We will express this expression in the standard form of complex number a+ ib. We will add real and…