(a) Find the modulus and argument of 1+√3i. (b) Hence find (1+√√3i) in the form rcise. 5 5 (c) Hence find (1+√3i) in simplified Cartesian for

Q: (b) Show that i10 is real, even though i or 10i is not.

A:

Q: 5(2-3i) – 4(4+6i)

A:

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

A: Given expression is 3-2i 1+5i5+2i -4-i. Simplify the above expression as follows.

Q: (5 – 6i) – (3 – 2i)

A: We have to perform the subtraction between two complex numbers.

Q: Q3: Express complex numbers to polarform and draw them: 1. 5+2i. 2. 4i

A: As we know that we can represent a complex number from rectangular to polar form as :- Rectangular…

Q: Find the value of q such that (3 + 4i)(1 + 2i) (1 + 3i) = q(1 + i).

A: We have to simplify left hand side expression then compare both side to find the value of q.

Q: Find the following: (a) (-1-i)7. (b) Square roots of 4√3+4i.

A:

Q: Write the following complex numbers in exponential form. The principal value of ал the argument…

A:

Q: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

A:

Q: Find all (real or complex) numbers z₁ and z2 such that 21+22=-6-3i Z1²2=3+11i

A: Given that:      z1+z2=-6-3iz1z2=3+11i The objective is to find all real and complex numbers z1  and…

Q: Find the modulus and argument of the following complex number. z= (3+2j) (- 1+2j), giving the…

A:

Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

A:

Q: Determine the product of (1+i) and (1-3i)

A:

Q: Find the distinct roots of (-7 + 2i)3/4

A: Let x= (-7 + 2i)3/4 ⇒x4=-7+2i3 On Simplifying, ⇒x4=-259+286i--(1) Let, x=u+iv Now,…

Q: (2i-9)2

A: We need to simplify (2i – 9)2 and express in the form of (a + ib). We can rewrite  (2i – 9)2 as (2i…

Q: Let z be a complex number, find therange of real values of a for which the equation. z+alz-1+2i=0has…

A:

Q: 11 (6i – 9) = Your answer should be a Complex number in the form a + bi where a and b are real…

A: Complex number multiply

Q: 4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 −…

A: We have to prove that any complex number of norm 1 (except -1) can be written in the form…

Q: a

A:

Q: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: If z1 =3 - 5i and z2 =26 -2i, find z1 +z2 and z1 -z2.

A: Given that, z1 = 3 - 5i z2 = 26 -2i We have to find z1 + z2 and z1 - z2.