Practice Problems and Examples for Complex Numbers

What are the three cube roots of -1?
Not sure if this is a trick question, But I have been asked this. one of the ansers is -1, what are the other 2?

2022-01-17

How to combine complex powers?
It is not posssible to combine complex powers in the usual way:
${(x^{y})}^{z} = x^{y z}$
There was mention of multi-valued functions, is there some theory that makes this all work out correctly?

2022-01-17

Why $\sqrt{- 1 \cdot - 1} \neq {\sqrt{- 1}}^{2} ?$

2022-01-17

What is $\sqrt{i}$ ?
If $i = \sqrt{- 1}$ is $\sqrt{i}$ imaginary?
Is it used or considered often in mathematics? How is it notated?

Chris Cruz 2022-01-17

Perform the indicated operation:
$7 [\cos (228^{\circ}) + i \sin (228^{\circ})] \times 8 [\cos (232^{\circ}) + i \sin (232^{\circ})]$

Shirley Thompson 2022-01-17

Multiply and simplify the following complex numbers:
$(- 3 + 3 i) \times (3 - 2 i)$

William Collins 2022-01-17

My work with complex numbers verified that the only possible cube root of 8 is 2. Determine whether the statement makes sense or does not make sense, and explain your reasoning.

kuhse4461a 2022-01-17

How do I solve $z^{2} = 2 + 2 r t 3 i$ ? For a quadratic I find $y^{2} - r t 2 y + 1 r t 3$ but my answer is nothing like a solve. Can someone advise?

elvishwitchxyp 2022-01-17

If $| Z 1 | = | Z 2 | and a r g z 1 \sim a r g z 2 = π$ , how do you show that $Z 1 + Z 2 = 0$ ?

Patricia Crane 2022-01-17

If $a + b + c = 0$ , and w is a complex root of cube roots of unity, then can you show that
${(a + b w + c w^{2})}^{3} + {(a + b w^{2} + c w)}^{3} = 27 a b c$ ?

Maria Huey 2022-01-17

How do I add the following? $Z 1 = 3 - \sqrt{- 2} and Z 2 = 4 + \sqrt{- 4}$ ?

John Stewart 2022-01-17

How do you show that the function $w = z e^{\overset{―}{z}}$ is nowhere analytic?

Reginald Metcalf 2022-01-17

Suppose $\frac{d}{d z} (f (z))$ exists at a point z. Is $\frac{d}{d z} (f (z))$ continuous at z?

tripiverded9 2022-01-17

What are the solutions for the equations $\cos Z = - i, 3 \sin Z + i \cos Z = e^{i z}, and e^{2 z} + 4 i = - 3 \sqrt{3} - 3 i$ ?

expeditiupc 2022-01-17

How do you simplify $\sqrt{- 4} - \sqrt{- 25}$ ?

osteoblogda 2022-01-17

How do you simplify $\sqrt{- 2156}$ ?

aspifsGak5u 2022-01-17

How do you find the absolute value of $5 + 12 i$ ?

Painevg 2022-01-17

How do you simplify $i^{6} (2 i - i^{2} - 3 i^{3})$ ?

Kathleen Rausch 2022-01-17

How do you simplify $(- 10 i) (9 i) + 8$ ?

Annette Sabin 2022-01-16

To determine:
$\frac{1 + i}{1 - i} + \frac{2}{1 + i}$ ?

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Precalculus

Understanding Complex Numbers - Examples and Equations