Question

Represent the following complex numbers on an Argand diagram, simplifying first, where necessary. In each case, calculate the modulus and the argument and write the number in modulus-argument form. b) $3 - \sqrt{3}i$ c) $-1 + \sqrt{3}i$ a) $1 + i$ d) $-2 - 2i$ e) $3 - 4i$ f) $-8 - 6i$ g) $5 + 12i$ h) $-24 + 10i$ i) $-2( -\frac{3}{2} + i)$ j) $\frac{-4 - 3i}{2}$ k) $2 + 9i - 3(i - 2)$ l) $(1 - 3i)(2 + i)$ o) $\frac{-32 - 43i}{(2 - 3i)^2}$ p) $(1 + i)^3$

          Represent the following complex numbers on an Argand diagram, simplifying first,
where necessary. In each case, calculate the modulus and the argument and write
the number in modulus-argument form.
b) $3 - \sqrt{3}i$
c) $-1 + \sqrt{3}i$
a) $1 + i$
d) $-2 - 2i$
e) $3 - 4i$
f) $-8 - 6i$
g) $5 + 12i$
h) $-24 + 10i$
i) $-2( -\frac{3}{2} + i)$
j) $\frac{-4 - 3i}{2}$
k) $2 + 9i - 3(i - 2)$
l) $(1 - 3i)(2 + i)$
o) $\frac{-32 - 43i}{(2 - 3i)^2}$
p) $(1 + i)^3$

Represent the following complex numbers on an Argand diagram, simplifying first,
where necessary. In each case, calculate the modulus and the argument and write
the number in modulus-argument form.
b) 3 - √(3)i
c) -1 + √(3)i
a) 1 + i
d) -2 - 2i
e) 3 - 4i
f) -8 - 6i
g) 5 + 12i
h) -24 + 10i
i) -2( -(3)/(2) + i)
j) (-4 - 3i)/(2)
k) 2 + 9i - 3(i - 2)
l) (1 - 3i)(2 + i)
o) (-32 - 43i)/((2 - 3i)^2)
p) (1 + i)^3

Added by Martin A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Craig West

Step 1

The modulus of 1+i is √2, and the argument is π/4. So, in modulus-argument form, 1+i can be written as √2(cos(π/4) + i sin(π/4)). Show more…

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Argand diagram, simplifying first. Represent the following complex numbers on an Argand diagram, calculate the modulus and the argument, and write the number in modulus-argument form: a) 1+i b) âˆš3i c) -1 + âˆš3i d) -2 + 2i e) 3 - 4i f) -8 - 6i g) 5 + 12i h) âˆš24 + 10i i) âˆš2(-2+i) j) 24-3i k) 2 + 9âˆš3 (i - 2) l) (1 + 5âˆš3i)(2 + i) m) (2 + i)^2 n) âˆš(332 - 43i) o) 3 - 4i (2 - 3i)^2 p) (1 + i)^3